List of all classes, functions and methods in pythonigraph
Lowlevel representation of a graph.
Don't use it directly, use igraph.Graph
instead.
Unknown Field: deffield  ref  Reference 
Method  vcount 
Counts the number of vertices. 
Method  ecount 
Counts the number of edges. 
Method  is_dag 
Checks whether the graph is a DAG (directed acyclic graph). 
Method  is_directed 
Checks whether the graph is directed. 
Method  is_simple 
Checks whether the graph is simple (no loop or multiple edges). 
Method  is_tree 
Checks whether the graph is a (directed or undirected) tree graph. 
Method  add_vertices 
Adds vertices to the graph. 
Method  delete_vertices 
Deletes vertices and all its edges from the graph. 
Method  add_edges 
Adds edges to the graph. 
Method  delete_edges 
Removes edges from the graph. 
Method  degree 
Returns some vertex degrees from the graph. 
Method  strength 
Returns the strength (weighted degree) of some vertices from the graph 
Method  is_loop 
Checks whether a specific set of edges contain loop edges 
Method  is_multiple 
Checks whether an edge is a multiple edge. 
Method  has_multiple 
Checks whether the graph has multiple edges. 
Method  is_mutual 
Checks whether an edge has an opposite pair. 
Method  count_multiple 
Counts the multiplicities of the given edges. 
Method  neighbors 
Returns adjacent vertices to a given vertex. 
Method  successors 
Returns the successors of a given vertex. 
Method  predecessors 
Returns the predecessors of a given vertex. 
Method  get_eid 
Returns the edge ID of an arbitrary edge between vertices v1 and v2 
Method  get_eids 
Returns the edge IDs of some edges between some vertices. 
Method  incident 
Returns the edges a given vertex is incident on. 
Method  Adjacency 
Generates a graph from its adjacency matrix. 
Method  Asymmetric_Preference 
Generates a graph based on asymmetric vertex types and connection probabilities. 
Method  Atlas 
Generates a graph from the Graph Atlas. 
Method  Barabasi 
Generates a graph based on the BarabasiAlbert model. 
Method  De_Bruijn 
Generates a de Bruijn graph with parameters (m, n) 
Method  Establishment 
Generates a graph based on a simple growing model with vertex types. 
Method  Erdos_Renyi 
Generates a graph based on the ErdosRenyi model. 
Method  Famous 
Generates a famous graph based on its name. 
Method  Forest_Fire 
Generates a graph based on the forest fire model 
Method  Full_Citation 
Generates a full citation graph 
Method  Full 
Generates a full graph (directed or undirected, with or without loops). 
Method  Growing_Random 
Generates a growing random graph. 
Method  Kautz 
Generates a Kautz graph with parameters (m, n) 
Method  K_Regular 
Generates a kregular random graph 
Method  Preference 
Generates a graph based on vertex types and connection probabilities. 
Method  Recent_Degree 
Generates a graph based on a stochastic model where the probability of an edge gaining a new node is proportional to the edges gained in a given time window. 
Method  SBM 
Generates a graph based on a stochastic blockmodel. 
Method  Star 
Generates a star graph. 
Method  Lattice 
Generates a regular lattice. 
Method  LCF 
Generates a graph from LCF notation. 
Method  Realize_Degree_Sequence 
Generates a graph from a degree sequence. 
Method  Ring 
Generates a ring graph. 
Method  Static_Fitness 
Generates a nongrowing graph with edge probabilities proportional to node fitnesses. 
Method  Static_Power_Law 
Generates a nongrowing graph with prescribed powerlaw degree distributions. 
Method  Tree 
Generates a tree in which almost all vertices have the same number of children. 
Method  Degree_Sequence 
Generates a graph with a given degree sequence. 
Method  Isoclass 
Generates a graph with a given isomorphism class. 
Method  Tree_Game 
Generates a random tree by sampling uniformly from the set of labelled trees with a given number of nodes. 
Method  Watts_Strogatz 
No summary 
Method  Weighted_Adjacency 
Generates a graph from its adjacency matrix. 
Method  are_connected 
Decides whether two given vertices are directly connected. 
Method  articulation_points 
Returns the list of articulation points in the graph. 
Method  assortativity 
Returns the assortativity of the graph based on numeric properties of the vertices. 
Method  assortativity_degree 
Returns the assortativity of a graph based on vertex degrees. 
Method  assortativity_nominal 
Returns the assortativity of the graph based on vertex categories. 
Method  average_path_length 
Calculates the average path length in a graph. 
Method  authority_score 
Calculates Kleinberg's authority score for the vertices of the graph 
Method  betweenness 
Calculates or estimates the betweenness of vertices in a graph. 
Method  biconnected_components 
Calculates the biconnected components of the graph. 
Method  bipartite_projection 
Internal function, undocumented. 
Method  bipartite_projection_size 
Internal function, undocumented. 
Method  bridges 
Returns the list of bridges in the graph. 
Method  chordal_completion 
chordal_complation(alpha=None, alpham1=None)  
Method  closeness 
Calculates the closeness centralities of given vertices in a graph. 
Method  harmonic_centrality 
Calculates the harmonic centralities of given vertices in a graph. 
Method  clusters 
Calculates the (strong or weak) clusters for a given graph. 
Method  copy 
Creates a copy of the graph. 
Method  decompose 
Decomposes the graph into subgraphs. 
Method  contract_vertices 
Contracts some vertices in the graph, i.e. replaces groups of vertices with single vertices. Edges are not affected. 
Method  constraint 
Calculates Burt's constraint scores for given vertices in a graph. 
Method  density 
Calculates the density of the graph. 
Method  diameter 
Calculates the diameter of the graph. 
Method  get_diameter 
Returns a path with the actual diameter of the graph. 
Method  farthest_points 
Returns two vertex IDs whose distance equals the actual diameter of the graph. 
Method  diversity 
Calculates the structural diversity index of the vertices. 
Method  eccentricity 
Calculates the eccentricities of given vertices in a graph. 
Method  edge_betweenness 
Calculates or estimates the edge betweennesses in a graph. 
Method  eigen_adjacency 
Undocumented 
Method  edge_connectivity 
Calculates the edge connectivity of the graph or between some vertices. 
Method  eigenvector_centrality 
Calculates the eigenvector centralities of the vertices in a graph. 
Method  feedback_arc_set 
Calculates an approximately or exactly minimal feedback arc set. 
Method  get_shortest_paths 
Calculates the shortest paths from/to a given node in a graph. 
Method  get_all_shortest_paths 
Calculates all of the shortest paths from/to a given node in a graph. 
Method  girth 
Returns the girth of the graph. 
Method  convergence_degree 
Undocumented (yet). 
Method  convergence_field_size 
Undocumented (yet). 
Method  hub_score 
Calculates Kleinberg's hub score for the vertices of the graph 
Method  induced_subgraph 
Returns a subgraph spanned by the given vertices. 
Method  is_bipartite 
Decides whether the graph is bipartite or not. 
Method  is_chordal 
Returns whether the graph is chordal or not. 
Method  knn 
Calculates the average degree of the neighbors for each vertex, and the same quantity as the function of vertex degree. 
Method  is_connected 
Decides whether the graph is connected. 
Method  linegraph 
Returns the line graph of the graph. 
Method  maxdegree 
Returns the maximum degree of a vertex set in the graph. 
Method  maximum_cardinality_search 
No summary 
Method  neighborhood 
No summary 
Method  neighborhood_size 
No summary 
Method  personalized_pagerank 
Calculates the personalized PageRank values of a graph. 
Method  path_length_hist 
Calculates the path length histogram of the graph @attention: this function is wrapped in a more convenient syntax in the derived class Graph . It is advised to use that instead of this version. 
Method  permute_vertices 
Permutes the vertices of the graph according to the given permutation and returns the new graph. 
Method  radius 
Calculates the radius of the graph. 
Method  reciprocity 
No summary 
Method  rewire 
Randomly rewires the graph while preserving the degree distribution. 
Method  rewire_edges 
Rewires the edges of a graph with constant probability. 
Method  shortest_paths 
Calculates shortest path lengths for given vertices in a graph. 
Method  simplify 
Simplifies a graph by removing selfloops and/or multiple edges. 
Method  subcomponent 
Determines the indices of vertices which are in the same component as a given vertex. 
Method  subgraph_edges 
Returns a subgraph spanned by the given edges. 
Method  topological_sorting 
Calculates a possible topological sorting of the graph. 
Method  to_prufer 
Converts a tree graph into a Prufer sequence. 
Method  transitivity_undirected 
Calculates the global transitivity (clustering coefficient) of the graph. 
Method  transitivity_local_undirected 
Calculates the local transitivity (clustering coefficient) of the given vertices in the graph. 
Method  transitivity_avglocal_undirected 
Calculates the average of the vertex transitivities of the graph. 
Method  unfold_tree 
Unfolds the graph using a BFS to a tree by duplicating vertices as necessary. 
Method  vertex_connectivity 
Calculates the vertex connectivity of the graph or between some vertices. 
Method  bibcoupling 
Calculates bibliographic coupling scores for given vertices in a graph. 
Method  cocitation 
Calculates cocitation scores for given vertices in a graph. 
Method  similarity_dice 
Dice similarity coefficient of vertices. 
Method  similarity_inverse_log_weighted 
Inverse logweighted similarity coefficient of vertices. 
Method  similarity_jaccard 
Jaccard similarity coefficient of vertices. 
Method  motifs_randesu 
Counts the number of motifs in the graph 
Method  motifs_randesu_no 
Counts the total number of motifs in the graph 
Method  motifs_randesu_estimate 
Counts the total number of motifs in the graph 
Method  dyad_census 
Dyad census, as defined by Holland and Leinhardt 
Method  triad_census 
Triad census, as defined by Davis and Leinhardt 
Method  layout_bipartite 
Place the vertices of a bipartite graph in two layers. 
Method  layout_circle 
Places the vertices of the graph uniformly on a circle or a sphere. 
Method  layout_grid 
Places the vertices of a graph in a 2D or 3D grid. 
Method  layout_star 
Calculates a starlike layout for the graph. 
Method  layout_kamada_kawai 
Places the vertices on a plane according to the KamadaKawai algorithm. 
Method  layout_davidson_harel 
Places the vertices on a 2D plane according to the DavidsonHarel layout algorithm. 
Method  layout_drl 
Places the vertices on a 2D plane or in the 3D space ccording to the DrL layout algorithm. 
Method  layout_fruchterman_reingold 
Places the vertices on a 2D plane according to the FruchtermanReingold algorithm. 
Method  layout_graphopt 
This is a port of the graphopt layout algorithm by Michael Schmuhl. graphopt version 0.4.1 was rewritten in C and the support for layers was removed. 
Method  layout_lgl 
Places the vertices on a 2D plane according to the Large Graph Layout. 
Method  layout_mds 
Places the vertices in an Euclidean space with the given number of dimensions using multidimensional scaling. 
Method  layout_reingold_tilford 
Places the vertices on a 2D plane according to the ReingoldTilford layout algorithm. 
Method  layout_reingold_tilford_circular 
Circular ReingoldTilford layout for trees. 
Method  layout_random 
Places the vertices of the graph randomly. 
Method  bfs 
Conducts a breadth first search (BFS) on the graph. 
Method  bfsiter 
Constructs a breadth first search (BFS) iterator of the graph. 
Method  dfsiter 
Constructs a depth first search (DFS) iterator of the graph. 
Method  get_adjacency 
Returns the adjacency matrix of a graph. 
Method  get_edgelist 
Returns the edge list of a graph. 
Method  get_incidence 
Internal function, undocumented. 
Method  to_directed 
Converts an undirected graph to directed. 
Method  to_undirected 
Converts a directed graph to undirected. 
Method  laplacian 
Returns the Laplacian matrix of a graph. 
Method  Read_DIMACS 
Reads a graph from a file conforming to the DIMACS minimumcost flow file format. 
Method  Read_DL 
Reads an UCINET DL file and creates a graph based on it. 
Method  Read_Edgelist 
Reads an edge list from a file and creates a graph based on it. 
Method  Read_GraphDB 
Reads a GraphDB format file and creates a graph based on it. 
Method  Read_GraphML 
Reads a GraphML format file and creates a graph based on it. 
Method  Read_GML 
Reads a GML file and creates a graph based on it. 
Method  Read_Ncol 
Reads an .ncol file used by LGL. 
Method  Read_Lgl 
Reads an .lgl file used by LGL. 
Method  Read_Pajek 
Reads a Pajek format file and creates a graph based on it. 
Method  write_dimacs 
Writes the graph in DIMACS format to the given file. 
Method  write_dot 
Writes the graph in DOT format to the given file. 
Method  write_edgelist 
Writes the edge list of a graph to a file. 
Method  write_gml 
Writes the graph in GML format to the given file. 
Method  write_ncol 
Writes the edge list of a graph to a file in .ncol format. 
Method  write_lgl 
Writes the edge list of a graph to a file in .lgl format. 
Method  write_pajek 
Writes the graph in Pajek format to the given file. 
Method  write_graphml 
Writes the graph to a GraphML file. 
Method  write_leda 
Writes the graph to a file in LEDA native format. 
Method  canonical_permutation 
Calculates the canonical permutation of a graph using the BLISS isomorphism algorithm. 
Method  isoclass 
Returns the isomorphism class of the graph or its subgraph. 
Method  isomorphic 
Checks whether the graph is isomorphic to another graph. 
Method  isomorphic_bliss 
Checks whether the graph is isomorphic to another graph, using the BLISS isomorphism algorithm. 
Method  isomorphic_vf2 
Checks whether the graph is isomorphic to another graph, using the VF2 isomorphism algorithm. 
Method  count_isomorphisms_vf2 
Determines the number of isomorphisms between the graph and another one 
Method  get_isomorphisms_vf2 
Returns all isomorphisms between the graph and another one 
Method  subisomorphic_vf2 
Checks whether a subgraph of the graph is isomorphic to another graph. 
Method  count_subisomorphisms_vf2 
Determines the number of subisomorphisms between the graph and another one 
Method  get_subisomorphisms_vf2 
Returns all subisomorphisms between the graph and another one 
Method  subisomorphic_lad 
Checks whether a subgraph of the graph is isomorphic to another graph. 
Method  get_subisomorphisms_lad 
Returns all subisomorphisms between the graph and another one using the LAD algorithm. 
Method  attributes 

Method  vertex_attributes 

Method  edge_attributes 

Method  complementer 
Returns the complementer of the graph 
Method  compose 
Returns the composition of two graphs. 
Method  difference 
Subtracts the given graph from the original 
Method  dominator 
Returns the dominator tree from the given root node 
Method  maxflow_value 
Returns the value of the maximum flow between the source and target vertices. 
Method  maxflow 
Returns the maximum flow between the source and target vertices. 
Method  all_st_cuts 
Returns all the cuts between the source and target vertices in a directed graph. 
Method  all_st_mincuts 
Returns all minimum cuts between the source and target vertices in a directed graph. 
Method  mincut_value 
Returns the minimum cut between the source and target vertices or within the whole graph. 
Method  mincut 
Calculates the minimum cut between the source and target vertices or within the whole graph. 
Method  st_mincut 
Calculates the minimum cut between the source and target vertices in a graph. 
Method  gomory_hu_tree 
Internal function, undocumented. 
Method  all_minimal_st_separators 
Returns a list containing all the minimal st separators of a graph. 
Method  is_minimal_separator 
Decides whether the given vertex set is a minimal separator. 
Method  is_separator 
Decides whether the removal of the given vertices disconnects the graph. 
Method  minimum_size_separators 
Returns a list containing all separator vertex sets of minimum size. 
Method  cohesive_blocks 
Calculates the cohesive block structure of the graph. 
Method  cliques 
Returns some or all cliques of the graph as a list of tuples. 
Method  largest_cliques 
Returns the largest cliques of the graph as a list of tuples. 
Method  maximal_cliques 
Returns the maximal cliques of the graph as a list of tuples. 
Method  clique_number 
Returns the clique number of the graph. 
Method  independent_vertex_sets 
Returns some or all independent vertex sets of the graph as a list of tuples. 
Method  largest_independent_vertex_sets 
Returns the largest independent vertex sets of the graph as a list of tuples. 
Method  maximal_independent_vertex_sets 
Returns the maximal independent vertex sets of the graph as a list of tuples. 
Method  independence_number 
Returns the independence number of the graph. 
Method  modularity 
Calculates the modularity of the graph with respect to some vertex types. 
Method  coreness 
Finds the coreness (shell index) of the vertices of the network. 
Method  community_fastgreedy 
Finds the community structure of the graph according to the algorithm of Clauset et al based on the greedy optimization of modularity. 
Method  community_infomap 
Finds the community structure of the network according to the Infomap method of Martin Rosvall and Carl T. Bergstrom. 
Method  community_label_propagation 
Finds the community structure of the graph according to the label propagation method of Raghavan et al. 
Method  community_leading_eigenvector 
A proper implementation of Newman's eigenvector community structure detection. Each split is done by maximizing the modularity regarding the original network. See the reference for details. 
Method  community_multilevel 
No summary 
Method  community_edge_betweenness 
No summary 
Method  community_optimal_modularity 
Calculates the optimal modularity score of the graph and the corresponding community structure. 
Method  community_spinglass 
Finds the community structure of the graph according to the spinglass community detection method of Reichardt & Bornholdt. 
Method  community_leiden 
Finds the community structure of the graph using the Leiden algorithm of Traag, van Eck & Waltman. 
Method  community_walktrap 
Finds the community structure of the graph according to the random walk method of Latapy & Pons. 
Method  random_walk 
Performs a random walk of a given length from a given node. 
Method  _Bipartite 
Internal function, undocumented. 
Method  _Full_Bipartite 
Internal function, undocumented. 
Method  _GRG 
Internal function, undocumented. 
Method  _Incidence 
Internal function, undocumented. 
Method  _Random_Bipartite 
Internal function, undocumented. 
Method  _get_all_simple_paths 
Internal function, undocumented. 
Method  _spanning_tree 
Internal function, undocumented. 
Method  _layout_sugiyama 
Internal function, undocumented. 
Method  _is_matching 
Internal function, undocumented. 
Method  _is_maximal_matching 
Internal function, undocumented. 
Method  _maximum_bipartite_matching 
Internal function, undocumented. 
Method  __graph_as_capsule 
__graph_as_capsule() 
Method  _raw_pointer 
Returns the memory address of the igraph graph encapsulated by the Python object as an ordinary Python integer. 
Method  __register_destructor 
Registers a destructor to be called when the object is freed by Python. This function should not be used directly by igraph users. 
Counts the number of vertices.
Returns  the number of vertices in the graph. (type: integer) 
Checks whether the graph is a DAG (directed acyclic graph).
A DAG is a directed graph with no directed cycles.
Returns  True if it is a DAG, False otherwise. (type: boolean) 
Checks whether the graph is directed.
Returns  True if it is directed, False otherwise. (type: boolean) 
Checks whether the graph is simple (no loop or multiple edges).
Returns  True if it is simple, False otherwise. (type: boolean) 
Checks whether the graph is a (directed or undirected) tree graph.
For directed trees, the function may require that the edges are oriented outwards from the root or inwards to the root, depending on the value of the mode
argument.
Parameters  mode  for directed graphs, specifies how the edge directions should be taken into account. "all" means that the edge directions must be ignored, "out" means that the edges must be oriented away from the root, "in" means that the edges must be oriented towards the root. Ignored for undirected graphs. 
Returns  True if the graph is a tree, False otherwise. (type: boolean) 
igraph.Graph
Adds vertices to the graph.
Parameters  n  the number of vertices to be added 
Deletes vertices and all its edges from the graph.
Parameters  vs  a single vertex ID or the list of vertex IDs to be deleted. No argument deletes all vertices. 
igraph.Graph
Adds edges to the graph.
Parameters  es  the list of edges to be added. Every edge is represented with a tuple, containing the vertex IDs of the two endpoints. Vertices are enumerated from zero. 
igraph.Graph
Removes edges from the graph.
All vertices will be kept, even if they lose all their edges. Nonexistent edges will be silently ignored.
Parameters  es  the list of edges to be removed. Edges are identifed by edge IDs. EdgeSeq objects are also accepted here. No argument deletes all edges. 
Returns some vertex degrees from the graph.
This method accepts a single vertex ID or a list of vertex IDs as a parameter, and returns the degree of the given vertices (in the form of a single integer or a list, depending on the input parameter).
Parameters  vertices  a single vertex ID or a list of vertex IDs 
mode  the type of degree to be returned ("out" for outdegrees, "in" for indegrees or "all" for the sum of them).  
loops  whether selfloops should be counted. 
Returns the strength (weighted degree) of some vertices from the graph
This method accepts a single vertex ID or a list of vertex IDs as a parameter, and returns the strength (that is, the sum of the weights of all incident edges) of the given vertices (in the form of a single integer or a list, depending on the input parameter).
Parameters  vertices  a single vertex ID or a list of vertex IDs 
mode  the type of degree to be returned ("out" for outdegrees, "in" for indegrees or "all" for the sum of them).  
loops  whether selfloops should be counted.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. ``None`` means to treat the graph as unweighted, falling back to ordinary degree calculations. 
Checks whether a specific set of edges contain loop edges
Parameters  edges  edge indices which we want to check. If None , all edges are checked. 
Returns  a list of booleans, one for every edge given 
Checks whether an edge is a multiple edge.
Also works for a set of edges  in this case, every edge is checked one by one. Note that if there are multiple edges going between a pair of vertices, there is always one of them that is not reported as multiple (only the others). This allows one to easily detect the edges that have to be deleted in order to make the graph free of multiple edges.
Parameters  edges  edge indices which we want to check. If None , all edges are checked. 
Returns  a list of booleans, one for every edge given 
Checks whether the graph has multiple edges.
Returns  True if the graph has at least one multiple edge, False otherwise. (type: boolean) 
Checks whether an edge has an opposite pair.
Also works for a set of edges  in this case, every edge is checked one by one. The result will be a list of booleans (or a single boolean if only an edge index is supplied), every boolean corresponding to an edge in the edge set supplied. True
is returned for a given edge a > b if there exists another edge b > a in the original graph (not the given edge set!). All edges in an undirected graph are mutual. In case there are multiple edges between a and b, it is enough to have at least one edge in either direction to report all edges between them as mutual, so the multiplicity of edges do not matter.
Parameters  edges  edge indices which we want to check. If None , all edges are checked. 
Returns  a list of booleans, one for every edge given 
Counts the multiplicities of the given edges.
Parameters  edges  edge indices for which we want to count their multiplicity. If None , all edges are counted. 
Returns  the multiplicities of the given edges as a list. 
Returns adjacent vertices to a given vertex.
Parameters  vertex  a vertex ID 
mode  whether to return only successors ("out" ), predecessors ("in" ) or both ("all" ). Ignored for undirected graphs. 
Returns the successors of a given vertex.
Equivalent to calling the neighbors()
method with type="out"
.
Returns the predecessors of a given vertex.
Equivalent to calling the neighbors()
method with type="in"
.
Returns the edge ID of an arbitrary edge between vertices v1 and v2
Parameters  v1  the ID or name of the first vertex 
v2  the ID or name of the second vertex  
directed  whether edge directions should be considered in directed graphs. The default is True . Ignored for undirected graphs.  
error  if True , an exception will be raised when the given edge does not exist. If False , 1 will be returned in that case.  
Returns  the edge ID of an arbitrary edge between vertices v1 and v2 
Returns the edge IDs of some edges between some vertices.
This method can operate in two different modes, depending on which of the keyword arguments pairs
and path
are given.
The method does not consider multiple edges; if there are multiple edges between a pair of vertices, only the ID of one of the edges is returned.
Parameters  pairs  a list of integer pairs. Each integer pair is considered as a sourcetarget vertex pair; the corresponding edge is looked up in the graph and the edge ID is returned for each pair. 
path  a list of vertex IDs. The list is considered as a continuous path from the first vertex to the last, passing through the intermediate vertices. The corresponding edge IDs between the first and the second, the second and the third and so on are looked up in the graph and the edge IDs are returned. If both path and pairs are given, the two lists are concatenated.  
directed  whether edge directions should be considered in directed graphs. The default is True . Ignored for undirected graphs.  
error  if True , an exception will be raised if a given edge does not exist. If False , 1 will be returned in that case.  
Returns  the edge IDs in a list 
Returns the edges a given vertex is incident on.
Parameters  vertex  a vertex ID 
mode  whether to return only successors ("out" ), predecessors ("in" ) or both ("all" ). Ignored for undirected graphs. 
Generates a graph from its adjacency matrix.
Parameters  matrix  the adjacency matrix 
mode  the mode to be used. Possible values are:

Generates a graph based on asymmetric vertex types and connection probabilities.
This is the asymmetric variant of Preference()
. A given number of vertices are generated. Every vertex is assigned to an "incoming" and an "outgoing" vertex type according to the given joint type probabilities. Finally, every vertex pair is evaluated and a directed edge is created between them with a probability depending on the "outgoing" type of the source vertex and the "incoming" type of the target vertex.
Parameters  n  the number of vertices in the graph 
type_dist_matrix  matrix giving the joint distribution of vertex types  
pref_matrix  matrix giving the connection probabilities for different vertex types.  
attribute  the vertex attribute name used to store the vertex types. If None , vertex types are not stored.  
loops  whether loop edges are allowed. 
Generates a graph from the Graph Atlas.
Parameters  idx  The index of the graph to be generated. Indices start from zero, graphs are listed:

Unknown Field: newfield  ref  Reference 
Unknown Field: ref  An Atlas of Graphs by Ronald C. Read and Robin J. Wilson, Oxford University Press, 1998. 
Generates a graph based on the BarabasiAlbert model.
Parameters  n  the number of vertices 
m  either the number of outgoing edges generated for each vertex or a list containing the number of outgoing edges for each vertex explicitly.  
outpref  True if the outdegree of a given vertex should also increase its citation probability (as well as its indegree), but it defaults to False .  
directed  True if the generated graph should be directed (default: False ).  
power  the power constant of the nonlinear model. It can be omitted, and in this case the usual linear model will be used.  
zero_appeal  the attractivity of vertices with degree zero.  
implementation  the algorithm to use to generate the network. Possible values are:
 
start_from  if given and not None , this must be another GraphBase object. igraph will use this graph as a starting point for the preferential attachment model.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Barabasi, AL and Albert, R. 1999. Emergence of scaling in random networks. Science, 286 509512. 
Internal function, undocumented.
See Also  Graph.Bipartite() 
Generates a de Bruijn graph with parameters (m, n)
A de Bruijn graph represents relationships between strings. An alphabet of m letters are used and strings of length n are considered. A vertex corresponds to every possible string and there is a directed edge from vertex v to vertex w if the string of v can be transformed into the string of w by removing its first letter and appending a letter to it.
Please note that the graph will have m^n vertices and even more edges, so probably you don't want to supply too big numbers for m and n.
Parameters  m  the size of the alphabet 
n  the length of the strings 
Generates a graph based on a simple growing model with vertex types.
A single vertex is added at each time step. This new vertex tries to connect to k vertices in the graph. The probability that such a connection is realized depends on the types of the vertices involved.
Parameters  n  the number of vertices in the graph 
k  the number of connections tried in each step  
type_dist  list giving the distribution of vertex types  
pref_matrix  matrix (list of lists) giving the connection probabilities for different vertex types  
directed  whether to generate a directed graph. 
Generates a graph based on the ErdosRenyi model.
Parameters  n  the number of vertices. 
p  the probability of edges. If given, m must be missing.  
m  the number of edges. If given, p must be missing.  
directed  whether to generate a directed graph.  
loops  whether selfloops are allowed. 
Generates a famous graph based on its name.
Several famous graphs are known to igraph
including (but not limited to) the Chvatal graph, the Petersen graph or the Tutte graph. This method generates one of them based on its name (case insensitive). See the documentation of the C interface of igraph
for the names available: https://igraph.org/c/doc.
Parameters  name  the name of the graph to be generated. 
Generates a graph based on the forest fire model
The forest fire model is a growing graph model. In every time step, a new vertex is added to the graph. The new vertex chooses an ambassador (or more than one if ambs>1) and starts a simulated forest fire at its ambassador(s). The fire spreads through the edges. The spreading probability along an edge is given by fw_prob. The fire may also spread backwards on an edge by probability fw_prob * bw_factor. When the fire ended, the newly added vertex connects to the vertices ``burned'' in the previous fire.
Parameters  n  the number of vertices in the graph 
fw_prob  forward burning probability  
bw_factor  ratio of backward and forward burning probability  
ambs  number of ambassadors chosen in each step  
directed  whether the graph will be directed 
Generates a full citation graph
A full citation graph is a graph where the vertices are indexed from 0 to n1 and vertex i has a directed edge towards all vertices with an index less than i.
Parameters  n  the number of vertices. 
directed  whether to generate a directed graph. 
Generates a full graph (directed or undirected, with or without loops).
Parameters  n  the number of vertices. 
directed  whether to generate a directed graph.  
loops  whether selfloops are allowed. 
Internal function, undocumented.
See Also  Graph.Full_Bipartite() 
Generates a growing random graph.
Parameters  n  The number of vertices in the graph 
m  The number of edges to add in each step (after adding a new vertex)  
directed  whether the graph should be directed.  
citation  whether the new edges should originate from the most recently added vertex. 
Internal function, undocumented.
See Also  Graph.Incidence() 
Generates a Kautz graph with parameters (m, n)
A Kautz graph is a labeled graph, vertices are labeled by strings of length n+1 above an alphabet with m+1 letters, with the restriction that every two consecutive letters in the string must be different. There is a directed edge from a vertex v to another vertex w if it is possible to transform the string of v into the string of w by removing the first letter and appending a letter to it.
Parameters  m  the size of the alphabet minus one 
n  the length of the strings minus one 
Generates a kregular random graph
A kregular random graph is a random graph where each vertex has degree k. If the graph is directed, both the indegree and the outdegree of each vertex will be k.
Parameters  n  The number of vertices in the graph 
k  The degree of each vertex if the graph is undirected, or the indegree and outdegree of each vertex if the graph is directed  
directed  whether the graph should be directed.  
multiple  whether it is allowed to create multiple edges. 
Generates a graph based on vertex types and connection probabilities.
This is practically the nongrowing variant of Establishment
. A given number of vertices are generated. Every vertex is assigned to a vertex type according to the given type probabilities. Finally, every vertex pair is evaluated and an edge is created between them with a probability depending on the types of the vertices involved.
Parameters  n  the number of vertices in the graph 
type_dist  list giving the distribution of vertex types  
pref_matrix  matrix giving the connection probabilities for different vertex types.  
attribute  the vertex attribute name used to store the vertex types. If None , vertex types are not stored.  
directed  whether to generate a directed graph.  
loops  whether loop edges are allowed. 
Internal function, undocumented.
See Also  Graph.Random_Bipartite() 
Generates a graph based on a stochastic model where the probability of an edge gaining a new node is proportional to the edges gained in a given time window.
Parameters  n  the number of vertices 
m  either the number of outgoing edges generated for each vertex or a list containing the number of outgoing edges for each vertex explicitly.  
window  size of the window in time steps  
outpref  True if the outdegree of a given vertex should also increase its citation probability (as well as its indegree), but it defaults to False .  
directed  True if the generated graph should be directed (default: False ).  
power  the power constant of the nonlinear model. It can be omitted, and in this case the usual linear model will be used. 
Generates a graph based on a stochastic blockmodel.
A given number of vertices are generated. Every vertex is assigned to a vertex type according to the given block sizes. Vertices of the same type will be assigned consecutive vertex IDs. Finally, every vertex pair is evaluated and an edge is created between them with a probability depending on the types of the vertices involved. The probabilities are taken from the preference matrix.
Parameters  n  the number of vertices in the graph 
pref_matrix  matrix giving the connection probabilities for different vertex types.  
block_sizes  list giving the number of vertices in each block; must sum up to n.  
directed  whether to generate a directed graph.  
loops  whether loop edges are allowed. 
Generates a star graph.
Parameters  n  the number of vertices in the graph 
mode  Gives the type of the star graph to create. Should be either "in", "out", "mutual" or "undirected"  
center  Vertex ID for the central vertex in the star. 
Generates a regular lattice.
Parameters  dim  list with the dimensions of the lattice 
nei  value giving the distance (number of steps) within which two vertices will be connected.  
directed  whether to create a directed graph.  
mutual  whether to create all connections as mutual in case of a directed graph.  
circular  whether the generated lattice is periodic. 
Generates a graph from LCF notation.
LCF is short for LederbergCoxeterFrucht, it is a concise notation for 3regular Hamiltonian graphs. It consists of three parameters, the number of vertices in the graph, a list of shifts giving additional edges to a cycle backbone and another integer giving how many times the shifts should be performed. See http://mathworld.wolfram.com/LCFNotation.html for details.
Parameters  n  the number of vertices 
shifts  the shifts in a list or tuple  
repeats  the number of repeats 
Generates a graph from a degree sequence.
This method implements a HavelHakimi style graph construction from a given degree sequence. In each step, the algorithm picks two vertices in a deterministic manner and connects them. The way the vertices are picked is defined by the method
parameter. The allowed edge types (i.e. whether multiple or loop edges are allowed) are specified in the allowed_edge_types
parameter.
Parameters  out  Undocumented 
in_  Undocumented  
allowed_edge_types  controls whether loops or multiedges are allowed during the generation process. Note that not all combinations are supported for all types of graphs; an exception will be raised for unsupported combinations. Possible values are:
 
method  controls how the vertices are selected during the generation process. Possible values are:
 
outdeg  the degree sequence of an undirected graph (if indeg=None), or the outdegree sequence of a directed graph.  
indeg  None to generate an undirected graph, the indegree sequence to generate a directed graph. 
Generates a ring graph.
Parameters  n  the number of vertices in the ring 
directed  whether to create a directed ring.  
mutual  whether to create mutual edges in a directed ring.  
circular  whether to create a closed ring. 
Generates a nongrowing graph with edge probabilities proportional to node fitnesses.
The algorithm randomly selects vertex pairs and connects them until the given number of edges are created. Each vertex is selected with a probability proportional to its fitness; for directed graphs, a vertex is selected as a source proportional to its outfitness and as a target proportional to its infitness.
Parameters  m  the number of edges in the graph 
fitness_out  a numeric vector with nonnegative entries, one for each vertex. These values represent the fitness scores (outfitness scores for directed graphs). fitness is an alias of this keyword argument.  
fitness_in  a numeric vector with nonnegative entries, one for each vertex. These values represent the infitness scores for directed graphs. For undirected graphs, this argument must be None .  
loops  whether loop edges are allowed.  
multiple  whether multiple edges are allowed.  
Returns  a directed or undirected graph with the prescribed powerlaw degree distributions. 
Generates a nongrowing graph with prescribed powerlaw degree distributions.
Parameters  n  the number of vertices in the graph 
m  the number of edges in the graph  
exponent_out  the exponent of the outdegree distribution, which must be between 2 and infinity (inclusive). When exponent_in is not given or negative, the graph will be undirected and this parameter specifies the degree distribution. exponent is an alias to this keyword argument.  
exponent_in  the exponent of the indegree distribution, which must be between 2 and infinity (inclusive) It can also be negative, in which case an undirected graph will be generated.  
loops  whether loop edges are allowed.  
multiple  whether multiple edges are allowed.  
finite_size_correction  whether to apply a finitesize correction to the generated fitness values for exponents less than 3. See the paper of Cho et al for more details.  
Returns  a directed or undirected graph with the prescribed powerlaw degree distributions.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Goh KI, Kahng B, Kim D: Universal behaviour of load distribution in scalefree networks. Phys Rev Lett 87(27):278701, 2001.  
Cho YS, Kim JS, Park J, Kahng B, Kim D: Percolation transitions in scalefree networks under the Achlioptas process. Phys Rev Lett 103:135702, 2009. 
Generates a tree in which almost all vertices have the same number of children.
Parameters  n  the number of vertices in the graph 
children  the number of children of a vertex in the graph  
type  determines whether the tree should be directed, and if this is the case, also its orientation. Must be one of "in" , "out" and "undirected" . 
Generates a graph with a given degree sequence.
Parameters  out  the outdegree sequence for a directed graph. If the indegree sequence is omitted, the generated graph will be undirected, so this will be the indegree sequence as well 
in_  the indegree sequence for a directed graph. If omitted, the generated graph will be undirected.  
method  the generation method to be used. One of the following:

Generates a graph with a given isomorphism class.
Parameters  n  the number of vertices in the graph (3 or 4) 
cls  the isomorphism class  
directed  whether the graph should be directed. 
Generates a random tree by sampling uniformly from the set of labelled trees with a given number of nodes.
Parameters  n  the number of vertices in the tree 
directed  whether the graph should be directed  
method  the generation method to be used. One of the following:

Parameters  dim  the dimension of the lattice 
size  the size of the lattice along all dimensions  
nei  value giving the distance (number of steps) within which two vertices will be connected.  
p  rewiring probability  
loops  specifies whether loop edges are allowed  
multiple  specifies whether multiple edges are allowed  
See Also  Lattice() , rewire() , rewire_edges() if more flexibility is needed  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Duncan J Watts and Steven H Strogatz: Collective dynamics of small world networks, Nature 393, 440442, 1998 
Generates a graph from its adjacency matrix.
Parameters  matrix  the adjacency matrix 
mode  the mode to be used. Possible values are:
 
attr  the name of the edge attribute that stores the edge weights.  
loops  whether to include loop edges. When False , the diagonal of the adjacency matrix will be ignored. 
Decides whether two given vertices are directly connected.
Parameters  v1  the ID or name of the first vertex 
v2  the ID or name of the second vertex  
Returns  True if there exists an edge from v1 to v2, False otherwise. 
Returns the list of articulation points in the graph.
A vertex is an articulation point if its removal increases the number of connected components in the graph.
Returns the assortativity of the graph based on numeric properties of the vertices.
This coefficient is basically the correlation between the actual connectivity patterns of the vertices and the pattern expected from the disribution of the vertex types.
See equation (21) in Newman MEJ: Mixing patterns in networks, Phys Rev E 67:026126 (2003) for the proper definition. The actual calculation is performed using equation (26) in the same paper for directed graphs, and equation (4) in Newman MEJ: Assortative mixing in networks, Phys Rev Lett 89:208701 (2002) for undirected graphs.
Parameters  types1  vertex types in a list or the name of a vertex attribute holding vertex types. Types are ideally denoted by numeric values. 
types2  in directed assortativity calculations, each vertex can have an outtype and an intype. In this case, types1 contains the outtypes and this parameter contains the intypes in a list or the name of a vertex attribute. If None , it is assumed to be equal to types1.  
directed  whether to consider edge directions or not.  
Returns  the assortativity coefficient  
See Also  assortativity_degree() when the types are the vertex degrees  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Newman MEJ: Mixing patterns in networks, Phys Rev E 67:026126, 2003.  
Newman MEJ: Assortative mixing in networks, Phys Rev Lett 89:208701, 
Returns the assortativity of a graph based on vertex degrees.
See assortativity()
for the details. assortativity_degree()
simply calls assortativity()
with the vertex degrees as types.
Parameters  directed  whether to consider edge directions for directed graphs or not. This argument is ignored for undirected graphs. 
Returns  the assortativity coefficient  
See Also  assortativity() 
Returns the assortativity of the graph based on vertex categories.
Assuming that the vertices belong to different categories, this function calculates the assortativity coefficient, which specifies the extent to which the connections stay within categories. The assortativity coefficient is one if all the connections stay within categories and minus one if all the connections join vertices of different categories. For a randomly connected network, it is asymptotically zero.
See equation (2) in Newman MEJ: Mixing patterns in networks, Phys Rev E 67:026126 (2003) for the proper definition.
Parameters  types  vertex types in a list or the name of a vertex attribute holding vertex types. Types should be denoted by numeric values. 
directed  whether to consider edge directions or not.  
Returns  the assortativity coefficient  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Newman MEJ: Mixing patterns in networks, Phys Rev E 67:026126, 2003. 
Calculates the average path length in a graph.
Parameters  directed  whether to consider directed paths in case of a directed graph. Ignored for undirected graphs. 
unconn  what to do when the graph is unconnected. If True , the average of the geodesic lengths in the components is calculated. Otherwise for all unconnected vertex pairs, a path length equal to the number of vertices is used.  
Returns  the average path length in the graph 
Calculates Kleinberg's authority score for the vertices of the graph
Parameters  weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
scale  whether to normalize the scores so that the largest one is 1.  
arpack_options  an ARPACKOptions object used to finetune the ARPACK eigenvector calculation. If omitted, the modulelevel variable called arpack_options is used.  
return_eigenvalue  whether to return the largest eigenvalue  
Returns  the authority scores in a list and optionally the largest eigenvalue as a second member of a tuple  
See Also  hub_score() 
Calculates or estimates the betweenness of vertices in a graph.
Keyword arguments:
Parameters  vertices  the vertices for which the betweennesses must be returned. If None , assumes all of the vertices in the graph. 
directed  whether to consider directed paths.  
cutoff  if it is an integer, only paths less than or equal to this length are considered, effectively resulting in an estimation of the betweenness for the given vertices. If None , the exact betweenness is returned.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
Returns  the (possibly estimated) betweenness of the given vertices in a list 
igraph.Graph
Calculates the biconnected components of the graph.
Components containing a single vertex only are not considered as being biconnected.
Parameters  return_articulation_points  whether to return the articulation points as well 
Returns  a list of lists containing edge indices making up spanning trees of the biconnected components (one spanning tree for each component) and optionally the list of articulation points 
igraph.Graph
Internal function, undocumented.
See Also  Graph.bipartite_projection() 
igraph.Graph
Internal function, undocumented.
See Also  Graph.bipartite_projection_size() 
Returns the list of bridges in the graph.
An edge is a bridge if its removal increases the number of (weakly) connected components in the graph.
chordal_complation(alpha=None, alpham1=None) 
Returns the list of edges needed to be added to the graph to make it chordal.
A graph is chordal if each of its cycles of four or more nodes has a chord, i.e. an edge joining two nodes that are not adjacent in the cycle. An equivalent definition is that any chordless cycles have at most three nodes.
The chordal completion of a graph is the list of edges that needed to be added to the graph to make it chordal. It is an empty list if the graph is already chordal.
Note that at the moment igraph does not guarantee that the returned chordal completion is minimal; there may exist a subset of the returned chordal completion that is still a valid chordal completion.
Parameters  alpha  the alpha vector from the result of calling maximum_cardinality_search() on the graph. Useful only if you already have the alpha vector; simply passing None here will make igraph calculate the alpha vector on its own. 
alpham1  the inverse alpha vector from the result of calling maximum_cardinality_search() on the graph. Useful only if you already have the inverse alpha vector; simply passing None here will make igraph calculate the inverse alpha vector on its own.  
Returns  the list of edges to add to the graph; each item in the list is a sourcetarget pair of vertex indices. 
Calculates the closeness centralities of given vertices in a graph.
The closeness centerality of a vertex measures how easily other vertices can be reached from it (or the other way: how easily it can be reached from the other vertices). It is defined as the number of vertices minus one divided by the sum of the lengths of all geodesics from/to the given vertex.
If the graph is not connected, and there is no path between two vertices, the number of vertices is used instead the length of the geodesic. This is always longer than the longest possible geodesic.
Parameters  vertices  the vertices for which the closenesses must be returned. If None , uses all of the vertices in the graph. 
mode  must be one of "in" , "out" and "all" . "in" means that the length of the incoming paths, "out" means that the length of the outgoing paths must be calculated. "all" means that both of them must be calculated.  
cutoff  if it is an integer, only paths less than or equal to this length are considered, effectively resulting in an estimation of the closeness for the given vertices (which is always an underestimation of the real closeness, since some vertex pairs will appear as disconnected even though they are connected).. If None , the exact closeness is returned.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
normalized  Whether to normalize the raw closeness scores by multiplying by the number of vertices minus one.  
Returns  the calculated closenesses in a list 
Calculates the harmonic centralities of given vertices in a graph.
The harmonic centerality of a vertex measures how easily other vertices can be reached from it (or the other way: how easily it can be reached from the other vertices). It is defined as the mean inverse distance to all other vertices.
If the graph is not connected, and there is no path between two vertices, the inverse distance is taken to be zero.
Parameters  vertices  the vertices for which the harmonic centrality must be returned. If None , uses all of the vertices in the graph. 
mode  must be one of "in" , "out" and "all" . "in" means that the length of the incoming paths, "out" means that the length of the outgoing paths must be calculated. "all" means that both of them must be calculated.  
cutoff  if it is not None , only paths less than or equal to this length are considered.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
normalized  Whether to normalize the result. If True, the result is the mean inverse path length to other vertices, i.e. it is normalized by the number of vertices minus one. If False, the result is the sum of inverse path lengths to other vertices.  
Returns  the calculated harmonic centralities in a list 
igraph.Graph
Calculates the (strong or weak) clusters for a given graph.
Parameters  mode  must be either "strong" or "weak" , depending on the clusters being sought. Optional, defaults to "strong" . 
Returns  the component index for every node in the graph.  
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a VertexClustering object. It is advised to use that. 
Creates a copy of the graph.
Attributes are copied by reference; in other words, if you use mutable Python objects as attribute values, these objects will still be shared between the old and new graph. You can use `deepcopy()` from the `copy` module if you need a truly deep copy of the graph.
Decomposes the graph into subgraphs.
Parameters  mode  must be either "strong" or "weak" , depending on the clusters being sought. Optional, defaults to "strong" . 
maxcompno  maximum number of components to return. None means all possible components.  
minelements  minimum number of vertices in a component. By setting this to 2, isolated vertices are not returned as separate components.  
Returns  a list of the subgraphs. Every returned subgraph is a copy of the original. 
Contracts some vertices in the graph, i.e. replaces groups of vertices with single vertices. Edges are not affected.
Parameters  mapping  numeric vector which gives the mapping between old and new vertex IDs. Vertices having the same new vertex ID in this vector will be remapped into a single new vertex. It is safe to pass the membership vector of a VertexClustering object here. 
combine_attrs  specifies how to combine the attributes of the vertices being collapsed into a single one. If it is None , all the attributes will be lost. If it is a function, the attributes of the vertices will be collected and passed on to that function which will return the new attribute value that has to be assigned to the single collapsed vertex. It can also be one of the following string constants which define builtin collapsing functions: sum , prod , mean , median , max , min , first , last , random . You can also specify different combination functions for different attributes by passing a dict here which maps attribute names to functions. See simplify() for more details.  
Returns  None .  
See Also  simplify() 
Calculates Burt's constraint scores for given vertices in a graph.
Burt's constraint is higher if ego has less, or mutually stronger related (i.e. more redundant) contacts. Burt's measure of constraint, C[i], of vertex i's ego network V[i], is defined for directed and valued graphs as follows:
C[i] = sum( sum( (p[i,q] p[q,j])^2, q in V[i], q != i,j ), j in V[], j != i)
for a graph of order (ie. number od vertices) N, where proportional tie strengths are defined as follows:
p[i,j]=(a[i,j]+a[j,i]) / sum(a[i,k]+a[k,i], k in V[i], k != i), a[i,j] are elements of A and the latter being the graph adjacency matrix.
For isolated vertices, constraint is undefined.
Parameters  vertices  the vertices to be analysed or None for all vertices. 
weights  weights associated to the edges. Can be an attribute name as well. If None , every edge will have the same weight.  
Returns  constraint scores for all given vertices in a matrix. 
Calculates the density of the graph.
Parameters  loops  whether to take loops into consideration. If True , the algorithm assumes that there might be some loops in the graph and calculates the density accordingly. If False , the algorithm assumes that there can't be any loops. 
Returns  the density of the graph. 
Calculates the diameter of the graph.
Parameters  directed  whether to consider directed paths. 
unconn  if True and the graph is unconnected, the longest geodesic within a component will be returned. If False and the graph is unconnected, the result is the number of vertices if there are no weights or infinity if there are weights.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
Returns  the diameter 
Returns a path with the actual diameter of the graph.
If there are many shortest paths with the length of the diameter, it returns the first one it founds.
Parameters  directed  whether to consider directed paths. 
unconn  if True and the graph is unconnected, the longest geodesic within a component will be returned. If False and the graph is unconnected, the result is the number of vertices if there are no weights or infinity if there are weights.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
Returns  the vertices in the path in order. 
Returns two vertex IDs whose distance equals the actual diameter of the graph.
If there are many shortest paths with the length of the diameter, it returns the first one it found.
Parameters  directed  whether to consider directed paths. 
unconn  if True and the graph is unconnected, the longest geodesic within a component will be returned. If False and the graph is unconnected, the result contains the number of vertices if there are no weights or infinity if there are weights.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
Returns  a triplet containing the two vertex IDs and their distance. The IDs are None if the graph is unconnected and unconn is False . 
Calculates the structural diversity index of the vertices.
The structural diversity index of a vertex is simply the (normalized) Shannon entropy of the weights of the edges incident on the vertex.
The measure is defined for undirected graphs only; edge directions are ignored.
Parameters  vertices  the vertices for which the diversity indices must be returned. If None , uses all of the vertices in the graph. 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
Returns  the calculated diversity indices in a list, or a single number if a single vertex was supplied.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Eagle N, Macy M and Claxton R: Network diversity and economic development, Science 328, 10291031, 2010. 
Calculates the eccentricities of given vertices in a graph.
The eccentricity of a vertex is calculated by measuring the shortest distance from (or to) the vertex, to (or from) all other vertices in the graph, and taking the maximum.
Parameters  vertices  the vertices for which the eccentricity scores must be returned. If None , uses all of the vertices in the graph. 
mode  must be one of "in" , "out" and "all" . "in" means that edge directions are followed; "out" means that edge directions are followed the opposite direction; "all" means that directions are ignored. The argument has no effect for undirected graphs.  
Returns  the calculated eccentricities in a list, or a single number if a single vertex was supplied. 
Calculates or estimates the edge betweennesses in a graph.
Parameters  directed  whether to consider directed paths. 
cutoff  if it is an integer, only paths less than or equal to this length are considered, effectively resulting in an estimation of the betweenness values. If None , the exact betweennesses are returned.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
Returns  a list with the (exact or estimated) edge betweennesses of all edges. 
Calculates the edge connectivity of the graph or between some vertices.
The edge connectivity between two given vertices is the number of edges that have to be removed in order to disconnect the two vertices into two separate components. This is also the number of edge disjoint directed paths between the vertices. The edge connectivity of the graph is the minimal edge connectivity over all vertex pairs.
This method calculates the edge connectivity of a given vertex pair if both the source and target vertices are given. If none of them is given (or they are both negative), the overall edge connectivity is returned.
Parameters  source  the source vertex involved in the calculation. 
target  the target vertex involved in the calculation.  
checks  if the whole graph connectivity is calculated and this is True , igraph performs some basic checks before calculation. If the graph is not strongly connected, then the connectivity is obviously zero. If the minimum degree is one, then the connectivity is also one. These simple checks are much faster than checking the entire graph, therefore it is advised to set this to True . The parameter is ignored if the connectivity between two given vertices is computed.  
Returns  the edge connectivity 
Calculates the eigenvector centralities of the vertices in a graph.
Eigenvector centrality is a measure of the importance of a node in a network. It assigns relative scores to all nodes in the network based on the principle that connections from highscoring nodes contribute more to the score of the node in question than equal connections from lowscoring nodes. In practice, the centralities are determined by calculating eigenvector corresponding to the largest positive eigenvalue of the adjacency matrix. In the undirected case, this function considers the diagonal entries of the adjacency matrix to be twice the number of selfloops on the corresponding vertex.
In the directed case, the left eigenvector of the adjacency matrix is calculated. In other words, the centrality of a vertex is proportional to the sum of centralities of vertices pointing to it.
Eigenvector centrality is meaningful only for connected graphs. Graphs that are not connected should be decomposed into connected components, and the eigenvector centrality calculated for each separately.
Parameters  directed  whether to consider edge directions in a directed graph. Ignored for undirected graphs. 
scale  whether to normalize the centralities so the largest one will always be 1.  
weights  edge weights given as a list or an edge attribute. If None , all edges have equal weight.  
return_eigenvalue  whether to return the actual largest eigenvalue along with the centralities  
arpack_options  an ARPACKOptions object that can be used to finetune the calculation. If it is omitted, the modulelevel variable called arpack_options is used.  
Returns  the eigenvector centralities in a list and optionally the largest eigenvalue (as a second member of a tuple) 
Calculates an approximately or exactly minimal feedback arc set.
A feedback arc set is a set of edges whose removal makes the graph acyclic. Since this is always possible by removing all the edges, we are in general interested in removing the smallest possible number of edges, or an edge set with as small total weight as possible. This method calculates one such edge set. Note that the task is trivial for an undirected graph as it is enough to find a spanning tree and then remove all the edges not in the spanning tree. Of course it is more complicated for directed graphs.
Parameters  weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. When given, the algorithm will strive to remove lightweight edges in order to minimize the total weight of the feedback arc set. 
method  the algorithm to use. "eades" uses the greedy cycle breaking heuristic of Eades, Lin and Smyth, which is linear in the number of edges but not necessarily optimal; however, it guarantees that the number of edges to be removed is smaller than E/2  V/6. "ip" uses an integer programming formulation which is guaranteed to yield an optimal result, but is too slow for large graphs.  
Returns  the IDs of the edges to be removed, in a list.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Eades P, Lin X and Smyth WF: A fast and effective heuristic for the feedback arc set problem. In: Proc Inf Process Lett 319323, 1993. 
Calculates the shortest paths from/to a given node in a graph.
Parameters  v  the source/destination for the calculated paths 
to  a vertex selector describing the destination/source for the calculated paths. This can be a single vertex ID, a list of vertex IDs, a single vertex name, a list of vertex names or a VertexSeq object. None means all the vertices.  
weights  edge weights in a list or the name of an edge attribute holding edge weights. If None , all edges are assumed to have equal weight.  
mode  the directionality of the paths. "in" means to calculate incoming paths, "out" means to calculate outgoing paths, "all" means to calculate both ones.  
output  determines what should be returned. If this is "vpath" , a list of vertex IDs will be returned, one path for each target vertex. For unconnected graphs, some of the list elements may be empty. Note that in case of mode="in" , the vertices in a path are returned in reversed order. If output="epath" , edge IDs are returned instead of vertex IDs.  
Returns  see the documentation of the output parameter. 
Calculates all of the shortest paths from/to a given node in a graph.
Parameters  v  the source for the calculated paths 
to  a vertex selector describing the destination for the calculated paths. This can be a single vertex ID, a list of vertex IDs, a single vertex name, a list of vertex names or a VertexSeq object. None means all the vertices.  
weights  edge weights in a list or the name of an edge attribute holding edge weights. If None , all edges are assumed to have equal weight.  
mode  the directionality of the paths. "in" means to calculate incoming paths, "out" means to calculate outgoing paths, "all" means to calculate both ones.  
Returns  all of the shortest path from the given node to every other reachable node in the graph in a list. Note that in case of mode="in" , the vertices in a path are returned in reversed order! 
Internal function, undocumented.
See Also  Graph.get_all_simple_paths() 
Returns the girth of the graph.
The girth of a graph is the length of the shortest circle in it.
Parameters  return_shortest_circle  whether to return one of the shortest circles found in the graph. 
Returns  the length of the shortest circle or (if return_shortest_circle ) is true, the shortest circle itself as a list 
Calculates Kleinberg's hub score for the vertices of the graph
Parameters  weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
scale  whether to normalize the scores so that the largest one is 1.  
arpack_options  an ARPACKOptions object used to finetune the ARPACK eigenvector calculation. If omitted, the modulelevel variable called arpack_options is used.  
return_eigenvalue  whether to return the largest eigenvalue  
Returns  the hub scores in a list and optionally the largest eigenvalue as a second member of a tuple  
See Also  authority_score() 
Returns a subgraph spanned by the given vertices.
Parameters  vertices  a list containing the vertex IDs which should be included in the result. 
implementation  the implementation to use when constructing the new subgraph. igraph includes two implementations at the moment. "copy_and_delete" copies the original graph and removes those vertices that are not in the given set. This is more efficient if the size of the subgraph is comparable to the original graph. The other implementation ("create_from_scratch" ) constructs the result graph from scratch and then copies the attributes accordingly. This is a better solution if the subgraph is relatively small, compared to the original graph. "auto" selects between the two implementations automatically, based on the ratio of the size of the subgraph and the size of the original graph.  
Returns  the subgraph 
Decides whether the graph is bipartite or not.
Vertices of a bipartite graph can be partitioned into two groups A and B in a way that all edges go between the two groups.
Parameters  return_types  if False , the method will simply return True or False depending on whether the graph is bipartite or not. If True , the actual group assignments are also returned as a list of boolean values. (Note that the group assignment is not unique, especially if the graph consists of multiple components, since the assignments of components are independent from each other). 
Returns  True if the graph is bipartite, False if not. If return_types is True , the group assignment is also returned. 
Returns whether the graph is chordal or not.
A graph is chordal if each of its cycles of four or more nodes has a chord, i.e. an edge joining two nodes that are not adjacent in the cycle. An equivalent definition is that any chordless cycles have at most three nodes.
Parameters  alpha  the alpha vector from the result of calling maximum_cardinality_search() on the graph. Useful only if you already have the alpha vector; simply passing None here will make igraph calculate the alpha vector on its own. 
alpham1  the inverse alpha vector from the result of calling maximum_cardinality_search() on the graph. Useful only if you already have the inverse alpha vector; simply passing None here will make igraph calculate the inverse alpha vector on its own.  
Returns  True if the graph is chordal, False otherwise. 
Calculates the average degree of the neighbors for each vertex, and the same quantity as the function of vertex degree.
Parameters  vids  the vertices for which the calculation is performed. None means all vertices. 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. If this is given, the vertex strength will be used instead of the vertex degree in the calculations, but the "ordinary" vertex degree will be used for the second (degree dependent) list in the result.  
Returns  two lists in a tuple. The first list contains the average degree of neighbors for each vertex, the second contains the average degree of neighbors as a function of vertex degree. The zeroth element of this list corresponds to vertices of degree 1. 
Decides whether the graph is connected.
Parameters  mode  whether we should calculate strong or weak connectivity. 
Returns  True if the graph is connected, False otherwise. 
Returns the line graph of the graph.
The line graph L(G) of an undirected graph is defined as follows: L(G) has one vertex for each edge in G and two vertices in L(G) are connected iff their corresponding edges in the original graph share an end point.
The line graph of a directed graph is slightly different: two vertices are connected by a directed edge iff the target of the first vertex's corresponding edge is the same as the source of the second vertex's corresponding edge.
Returns the maximum degree of a vertex set in the graph.
This method accepts a single vertex ID or a list of vertex IDs as a parameter, and returns the degree of the given vertices (in the form of a single integer or a list, depending on the input parameter).
Parameters  vertices  a single vertex ID or a list of vertex IDs, or None meaning all the vertices in the graph. 
mode  the type of degree to be returned ("out" for outdegrees, "in" IN for indegrees or "all" for the sum of them).  
loops  whether selfloops should be counted. 
Conducts a maximum cardinality search on the graph. The function computes a rank alpha for each vertex such that visiting vertices in decreasing rank order corresponds to always choosing the vertex with the most already visited neighbors as the next one to visit.
Maximum cardinality search is useful in deciding the chordality of a graph: a graph is chordal if and only if any two neighbors of a vertex that are higher in rank than the original vertex are connected to each other.
The result of this function can be passed to is_chordal()
to speed up the chordality computation if you also need the result of the maximum cardinality search for other purposes.
Returns  a tuple consisting of the rank vector and its inverse. 
For each vertex specified by vertices, returns the vertices reachable from that vertex in at most order steps. If mindist is larger than zero, vertices that are reachable in less than mindist steps are excluded.
Parameters  vertices  a single vertex ID or a list of vertex IDs, or None meaning all the vertices in the graph. 
order  the order of the neighborhood, i.e. the maximum number of steps to take from the seed vertex.  
mode  specifies how to take into account the direction of the edges if a directed graph is analyzed. "out" means that only the outgoing edges are followed, so all vertices reachable from the source vertex in at most order steps are counted. "in" means that only the incoming edges are followed (in reverse direction of course), so all vertices from which the source vertex is reachable in at most order steps are counted. "all" treats directed edges as undirected.  
mindist  the minimum distance required to include a vertex in the result. If this is one, the seed vertex is not included. If this is two, the direct neighbors of the seed vertex are not included either, and so on.  
Returns  a single list specifying the neighborhood if vertices was an integer specifying a single vertex index, or a list of lists if vertices was a list or None . 
For each vertex specified by vertices, returns the number of vertices reachable from that vertex in at most order steps. If mindist is larger than zero, vertices that are reachable in less than mindist steps are excluded.
Parameters  vertices  a single vertex ID or a list of vertex IDs, or None meaning all the vertices in the graph. 
order  the order of the neighborhood, i.e. the maximum number of steps to take from the seed vertex.  
mode  specifies how to take into account the direction of the edges if a directed graph is analyzed. "out" means that only the outgoing edges are followed, so all vertices reachable from the source vertex in at most order steps are counted. "in" means that only the incoming edges are followed (in reverse direction of course), so all vertices from which the source vertex is reachable in at most order steps are counted. "all" treats directed edges as undirected.  
mindist  the minimum distance required to include a vertex in the result. If this is one, the seed vertex is not counted. If this is two, the direct neighbors of the seed vertex are not counted either, and so on.  
Returns  a single number specifying the neighborhood size if vertices was an integer specifying a single vertex index, or a list of sizes if vertices was a list or None . 
Calculates the personalized PageRank values of a graph.
The personalized PageRank calculation is similar to the PageRank calculation, but the random walk is reset to a nonuniform distribution over the vertices in every step with probability 1damping instead of a uniform distribution.
Parameters  vertices  the indices of the vertices being queried. None means all of the vertices. 
directed  whether to consider directed paths.  
damping  the damping factor. 1damping is the PageRank value for vertices with no incoming links.  
reset  the distribution over the vertices to be used when resetting the random walk. Can be a sequence, an iterable or a vertex attribute name as long as they return a list of floats whose length is equal to the number of vertices. If None , a uniform distribution is assumed, which makes the method equivalent to the original PageRank algorithm.  
reset_vertices  an alternative way to specify the distribution over the vertices to be used when resetting the random walk. Simply supply a list of vertex IDs here, or a VertexSeq or a Vertex . Resetting will take place using a uniform distribution over the specified vertices.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
arpack_options  an ARPACKOptions object used to finetune the ARPACK eigenvector calculation. If omitted, the modulelevel variable called arpack_options is used. This argument is ignored if not the ARPACK implementation is used, see the implementation argument.  
implementation  which implementation to use to solve the PageRank eigenproblem. Possible values are:
 
niter  The number of iterations to use in the power method implementation. It is ignored in the other implementations.  
eps  The power method implementation will consider the calculation as complete if the difference of PageRank values between iterations change less than this value for every node. It is ignored by the other implementations.  
Returns  a list with the personalized PageRank values of the specified vertices. 
igraph.Graph
Calculates the path length histogram of the graph
Parameters  directed  whether to consider directed paths 
Returns  a tuple. The first item of the tuple is a list of path lengths, the ith element of the list contains the number of paths with length i+1. The second item contains the number of unconnected vertex pairs as a float (since it might not fit into an integer)  
Unknown Field: attention  this function is wrapped in a more convenient syntax in the derived class Graph . It is advised to use that instead of this version. 
Permutes the vertices of the graph according to the given permutation and returns the new graph.
Vertex k of the original graph will become vertex permutation[k] in the new graph. No validity checks are performed on the permutation vector.
Returns  the new graph 
Calculates the radius of the graph.
The radius of a graph is defined as the minimum eccentricity of its vertices (see eccentricity()
).
Parameters  mode  what kind of paths to consider for the calculation in case of directed graphs. OUT considers paths that follow edge directions, IN considers paths that follow the opposite edge directions, ALL ignores edge directions. The argument is ignored for undirected graphs. 
Returns  the radius  
See Also  eccentricity() 
Reciprocity defines the proportion of mutual connections in a directed graph. It is most commonly defined as the probability that the opposite counterpart of a directed edge is also included in the graph. This measure is calculated if mode
is "default"
.
Prior to igraph 0.6, another measure was implemented, defined as the probability of mutual connection between a vertex pair if we know that there is a (possibly nonmutual) connection between them. In other words, (unordered) vertex pairs are classified into three groups: (1) disconnected, (2) nonreciprocally connected and (3) reciprocally connected. The result is the size of group (3), divided by the sum of sizes of groups (2) and (3). This measure is calculated if mode
is "ratio"
.
Parameters  ignore_loops  whether loop edges should be ignored. 
mode  the algorithm to use to calculate the reciprocity; see above for more details.  
Returns  the reciprocity of the graph 
Randomly rewires the graph while preserving the degree distribution.
Please note that the rewiring is done "inplace", so the original graph will be modified. If you want to preserve the original graph, use the copy
method before.
Parameters  n  the number of rewiring trials. 
mode  the rewiring algorithm to use. It can either be "simple" or "loops" ; the former does not create or destroy loop edges while the latter does. 
Rewires the edges of a graph with constant probability.
Each endpoint of each edge of the graph will be rewired with a constant probability, given in the first argument.
Please note that the rewiring is done "inplace", so the original graph will be modified. If you want to preserve the original graph, use the copy
method before.
Parameters  prob  rewiring probability 
loops  whether the algorithm is allowed to create loop edges  
multiple  whether the algorithm is allowed to create multiple edges. 
Calculates shortest path lengths for given vertices in a graph.
The algorithm used for the calculations is selected automatically: a simple BFS is used for unweighted graphs, Dijkstra's algorithm is used when all the weights are positive. Otherwise, the BellmanFord algorithm is used if the number of requested source vertices is larger than 100 and Johnson's algorithm is used otherwise.
Parameters  source  a list containing the source vertex IDs which should be included in the result. If None , all vertices will be considered. 
target  a list containing the target vertex IDs which should be included in the result. If None , all vertices will be considered.  
weights  a list containing the edge weights. It can also be an attribute name (edge weights are retrieved from the given attribute) or None (all edges have equal weight).  
mode  the type of shortest paths to be used for the calculation in directed graphs. "out" means only outgoing, "in" means only incoming paths. "all" means to consider the directed graph as an undirected one.  
Returns  the shortest path lengths for given vertices in a matrix 
Simplifies a graph by removing selfloops and/or multiple edges.
For example, suppose you have a graph with an edge attribute named weight
. graph.simplify(combine_edges=max)
will take the maximum of the weights of multiple edges and assign that weight to the collapsed edge. graph.simplify(combine_edges=sum)
will take the sum of the weights. You can also write graph.simplify(combine_edges=dict(weight="sum"))
or graph.simplify(combine_edges=dict(weight=sum))
, since sum
is recognised both as a Python builtin function and as a string constant.
Parameters  multiple  whether to remove multiple edges. 
loops  whether to remove loops.  
combine_edges  specifies how to combine the attributes of multiple edges between the same pair of vertices into a single attribute. If it is None , only one of the edges will be kept and all the attributes will be lost. If it is a function, the attributes of multiple edges will be collected and passed on to that function which will return the new attribute value that has to be assigned to the single collapsed edge. It can also be one of the following string constants:
You can also use a dict mapping edge attribute names to functions or the above string constants if you want to make the behaviour of the simplification process depend on the name of the attribute. 
Determines the indices of vertices which are in the same component as a given vertex.
Parameters  v  the index of the vertex used as the source/destination 
mode  if equals to "in" , returns the vertex IDs from where the given vertex can be reached. If equals to "out" , returns the vertex IDs which are reachable from the given vertex. If equals to "all" , returns all vertices within the same component as the given vertex, ignoring edge directions. Note that this is not equal to calculating the union of the results of "in" and "out" .  
Returns  the indices of vertices which are in the same component as a given vertex. 
Returns a subgraph spanned by the given edges.
Parameters  edges  a list containing the edge IDs which should be included in the result. 
delete_vertices  if True , vertices not incident on any of the specified edges will be deleted from the result. If False , all vertices will be kept.  
Returns  the subgraph 
Calculates a possible topological sorting of the graph.
Returns a partial sorting and issues a warning if the graph is not a directed acyclic graph.
Parameters  mode  if "out" , vertices are returned according to the forward topological order  all vertices come before their successors. If "in" , all vertices come before their ancestors. 
Returns  a possible topological ordering as a list 
Calculates the global transitivity (clustering coefficient) of the graph.
The transitivity measures the probability that two neighbors of a vertex are connected. More precisely, this is the ratio of the triangles and connected triplets in the graph. The result is a single real number. Directed graphs are considered as undirected ones.
Note that this measure is different from the local transitivity measure (see transitivity_local_undirected()
) as it calculates a single value for the whole graph.
Parameters  mode  if TRANSITIVITY_ZERO or "zero" , the result will be zero if the graph does not have any triplets. If "nan" or TRANSITIVITY_NAN , the result will be NaN (not a number). 
Returns  the transitivity  
See Also  transitivity_local_undirected() , transitivity_avglocal_undirected()  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  S. Wasserman and K. Faust: Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press, 1994. 
Calculates the local transitivity (clustering coefficient) of the given vertices in the graph.
The transitivity measures the probability that two neighbors of a vertex are connected. In case of the local transitivity, this probability is calculated separately for each vertex.
Note that this measure is different from the global transitivity measure (see transitivity_undirected()
) as it calculates a transitivity value for each vertex individually.
The traditional local transitivity measure applies for unweighted graphs only. When the weights
argument is given, this function calculates the weighted local transitivity proposed by Barrat et al (see references).
Parameters  vertices  a list containing the vertex IDs which should be included in the result. None means all of the vertices. 
mode  defines how to treat vertices with degree less than two. If TRANSITIVITT_ZERO or "zero" , these vertices will have zero transitivity. If TRANSITIVITY_NAN or "nan" , these vertices will have NaN (not a number) as their transitivity.  
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name.  
Returns  the transitivities for the given vertices in a list  
See Also  transitivity_undirected() , transitivity_avglocal_undirected()  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Watts DJ and Strogatz S: Collective dynamics of smallworld networks. Nature 393(6884):440442, 1998.  
Barrat A, Barthelemy M, PastorSatorras R and Vespignani A: The architecture of complex weighted networks. PNAS 101, 3747 (2004). http://arxiv.org/abs/condmat/0311416. 
igraph.Graph
Calculates the average of the vertex transitivities of the graph.
The transitivity measures the probability that two neighbors of a vertex are connected. In case of the average local transitivity, this probability is calculated for each vertex and then the average is taken. Vertices with less than two neighbors require special treatment, they will either be left out from the calculation or they will be considered as having zero transitivity, depending on the mode parameter.
Note that this measure is different from the global transitivity measure (see transitivity_undirected()
) as it simply takes the average local transitivity across the whole network.
Parameters  mode  defines how to treat vertices with degree less than two. If TRANSITIVITT_ZERO or "zero" , these vertices will have zero transitivity. If TRANSITIVITY_NAN or "nan" , these vertices will be excluded from the average. 
See Also  transitivity_undirected() , transitivity_local_undirected()  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  D. J. Watts and S. Strogatz: Collective dynamics of smallworld networks. Nature 393(6884):440442, 1998. 
Unfolds the graph using a BFS to a tree by duplicating vertices as necessary.
Parameters  sources  the source vertices to start the unfolding from. It should be a list of vertex indices, preferably one vertex from each connected component. You can use topological_sorting() to determine a suitable set. A single vertex index is also accepted. 
mode  which edges to follow during the BFS. OUT follows outgoing edges, IN follows incoming edges, ALL follows both. Ignored for undirected graphs.  
Returns  the unfolded tree graph and a mapping from the new vertex indices to the old ones. 
Calculates the vertex connectivity of the graph or between some vertices.
The vertex connectivity between two given vertices is the number of vertices that have to be removed in order to disconnect the two vertices into two separate components. This is also the number of vertex disjoint directed paths between the vertices (apart from the source and target vertices of course). The vertex connectivity of the graph is the minimal vertex connectivity over all vertex pairs.
This method calculates the vertex connectivity of a given vertex pair if both the source and target vertices are given. If none of them is given (or they are both negative), the overall vertex connectivity is returned.
Parameters  source  the source vertex involved in the calculation. 
target  the target vertex involved in the calculation.  
checks  if the whole graph connectivity is calculated and this is True , igraph performs some basic checks before calculation. If the graph is not strongly connected, then the connectivity is obviously zero. If the minimum degree is one, then the connectivity is also one. These simple checks are much faster than checking the entire graph, therefore it is advised to set this to True . The parameter is ignored if the connectivity between two given vertices is computed.  
neighbors  tells igraph what to do when the two vertices are connected. "error" raises an exception, "infinity" returns infinity, "ignore" ignores the edge.  
Returns  the vertex connectivity 
Calculates bibliographic coupling scores for given vertices in a graph.
Parameters  vertices  the vertices to be analysed. If None , all vertices will be considered. 
Returns  bibliographic coupling scores for all given vertices in a matrix. 
Calculates cocitation scores for given vertices in a graph.
Parameters  vertices  the vertices to be analysed. If None , all vertices will be considered. 
Returns  cocitation scores for all given vertices in a matrix. 
Dice similarity coefficient of vertices.
The Dice similarity coefficient of two vertices is twice the number of their common neighbors divided by the sum of their degrees. This coefficient is very similar to the Jaccard coefficient, but usually gives higher similarities than its counterpart.
Parameters  vertices  the vertices to be analysed. If None and pairs is also None , all vertices will be considered. 
pairs  the vertex pairs to be analysed. If this is given, vertices must be None , and the similarity values will be calculated only for the given pairs. Vertex pairs must be specified as tuples of vertex IDs.  
mode  which neighbors should be considered for directed graphs. Can be "all" , "in" or "out" , ignored for undirected graphs.  
loops  whether vertices should be considered adjacent to themselves. Setting this to True assumes a loop edge for all vertices even if none is present in the graph. Setting this to False may result in strange results: nonadjacent vertices may have larger similarities compared to the case when an edge is added between them  however, this might be exactly the result you want to get.  
Returns  the pairwise similarity coefficients for the vertices specified, in the form of a matrix if pairs is None or in the form of a list if pairs is not None . 
Inverse logweighted similarity coefficient of vertices.
Each vertex is assigned a weight which is 1 / log(degree). The logweighted similarity of two vertices is the sum of the weights of their common neighbors.
Parameters  vertices  the vertices to be analysed. If None , all vertices will be considered. 
mode  which neighbors should be considered for directed graphs. Can be "all" , "in" or "out" , ignored for undirected graphs. "in" means that the weights are determined by the outdegrees, "out" means that the weights are determined by the indegrees.  
Returns  the pairwise similarity coefficients for the vertices specified, in the form of a matrix (list of lists). 
Jaccard similarity coefficient of vertices.
The Jaccard similarity coefficient of two vertices is the number of their common neighbors divided by the number of vertices that are adjacent to at least one of them.
Parameters  vertices  the vertices to be analysed. If None and pairs is also None , all vertices will be considered. 
pairs  the vertex pairs to be analysed. If this is given, vertices must be None , and the similarity values will be calculated only for the given pairs. Vertex pairs must be specified as tuples of vertex IDs.  
mode  which neighbors should be considered for directed graphs. Can be "all" , "in" or "out" , ignored for undirected graphs.  
loops  whether vertices should be considered adjacent to themselves. Setting this to True assumes a loop edge for all vertices even if none is present in the graph. Setting this to False may result in strange results: nonadjacent vertices may have larger similarities compared to the case when an edge is added between them  however, this might be exactly the result you want to get.  
Returns  the pairwise similarity coefficients for the vertices specified, in the form of a matrix if pairs is None or in the form of a list if pairs is not None . 
Counts the number of motifs in the graph
Motifs are small subgraphs of a given structure in a graph. It is argued that the motif profile (ie. the number of different motifs in the graph) is characteristic for different types of networks and network function is related to the motifs in the graph.
This function is able to find the different motifs of size three and four (ie. the number of different subgraphs with three and four vertices) in the network.
In a big network the total number of motifs can be very large, so it takes a lot of time to find all of them. In such cases, a sampling method can be used. This function is capable of doing sampling via the cut_prob argument. This argument gives the probability that a branch of the motif search tree will not be explored.
Parameters  size  the size of the motifs (3 or 4). 
cut_prob  the cut probabilities for different levels of the search tree. This must be a list of length size or None to find all motifs.  
callback  None or a callable that will be called for every motif found in the graph. The callable must accept three parameters: the graph itself, the list of vertices in the motif and the isomorphism class of the motif (see isoclass() ). The search will stop when the callback returns an object with a nonzero truth value or raises an exception.  
Returns  the list of motifs if callback is None , or None otherwise  
See Also  Graph.motifs_randesu_no()  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  S. Wernicke and F. Rasche: FANMOD: a tool for fast network motif detection, Bioinformatics 22(9), 11521153, 2006. 
Counts the total number of motifs in the graph
Motifs are small subgraphs of a given structure in a graph. This function counts the total number of motifs in a graph without assigning isomorphism classes to them.
Parameters  size  the size of the motifs (3 or 4). 
cut_prob  the cut probabilities for different levels of the search tree. This must be a list of length size or None to find all motifs.  
See Also  Graph.motifs_randesu()  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  S. Wernicke and F. Rasche: FANMOD: a tool for fast network motif detection, Bioinformatics 22(9), 11521153, 2006. 
Counts the total number of motifs in the graph
Motifs are small subgraphs of a given structure in a graph. This function estimates the total number of motifs in a graph without assigning isomorphism classes to them by extrapolating from a random sample of vertices.
Parameters  size  the size of the motifs (3 or 4). 
cut_prob  the cut probabilities for different levels of the search tree. This must be a list of length size or None to find all motifs.  
sample  the size of the sample or the vertex IDs of the vertices to be used for sampling.  
See Also  Graph.motifs_randesu()  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  S. Wernicke and F. Rasche: FANMOD: a tool for fast network motif detection, Bioinformatics 22(9), 11521153, 2006. 
igraph.Graph
Dyad census, as defined by Holland and Leinhardt
Dyad census means classifying each pair of vertices of a directed graph into three categories: mutual, there is an edge from a to b and also from b to a; asymmetric, there is an edge either from a to b or from b to a but not the other way and null, no edges between a and b.
Returns  the number of mutual, asymmetric and null connections in a 3tuple.  
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a DyadCensus object. It is advised to use that. 
igraph.Graph
Triad census, as defined by Davis and Leinhardt
Calculating the triad census means classifying every triplets of vertices in a directed graph. A triplet can be in one of 16 states, these are listed in the documentation of the C interface of igraph.
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a TriadCensus object. It is advised to use that. The name of the triplet classes are also documented there. 
Place the vertices of a bipartite graph in two layers.
The layout is created by placing the vertices in two rows, according to their types. The positions of the vertices within the rows are then optimized to minimize the number of edge crossings using the heuristic used by the Sugiyama layout algorithm.
Parameters  types  an igraph vector containing the vertex types, or an attribute name. Anything that evalulates to False corresponds to vertices of the first kind, everything else to the second kind. 
hgap  minimum horizontal gap between vertices in the same layer.  
vgap  vertical gap between the two layers.  
maxiter  maximum number of iterations to take in the crossing reduction step. Increase this if you feel that you are getting too many edge crossings.  
Returns  the calculated layout. 
Places the vertices of the graph uniformly on a circle or a sphere.
Parameters  dim  the desired number of dimensions for the layout. dim=2 means a 2D layout, dim=3 means a 3D layout. 
order  the order in which the vertices are placed along the circle. Not supported when dim is not equal to 2.  
Returns  the calculated layout. 
Places the vertices of a graph in a 2D or 3D grid.
Parameters  width  the number of vertices in a single row of the layout. Zero or negative numbers mean that the width should be determined automatically. 
height  the number of vertices in a single column of the layout. Zero or negative numbers mean that the height should be determined automatically. It must not be given if the number of dimensions is 2.  
dim  the desired number of dimensions for the layout. dim=2 means a 2D layout, dim=3 means a 3D layout.  
Returns  the calculated layout. 
Calculates a starlike layout for the graph.
Parameters  center  the ID of the vertex to put in the center 
order  a numeric vector giving the order of the vertices (including the center vertex!). If it is None , the vertices will be placed in increasing vertex ID order.  
Returns  the calculated layout. 
Places the vertices on a plane according to the KamadaKawai algorithm.
This is a force directed layout, see Kamada, T. and Kawai, S.: An Algorithm for Drawing General Undirected Graphs. Information Processing Letters, 31/1, 715, 1989.
Parameters  maxiter  the maximum number of iterations to perform. 
epsilon  quit if the energy of the system changes less than epsilon. See the original paper for details.  
kkconst  the KamadaKawai vertex attraction constant. None means the square of the number of vertices.  
seed  if None , uses a random starting layout for the algorithm. If a matrix (list of lists), uses the given matrix as the starting position.  
minx  if not None , it must be a vector with exactly as many elements as there are vertices in the graph. Each element is a minimum constraint on the X value of the vertex in the layout.  
maxx  similar to minx, but with maximum constraints  
miny  similar to minx, but with the Y coordinates  
maxy  similar to maxx, but with the Y coordinates  
minz  similar to minx, but with the Z coordinates. Use only for 3D layouts (dim =3).  
maxz  similar to maxx, but with the Z coordinates. Use only for 3D layouts (dim =3).  
dim  the desired number of dimensions for the layout. dim=2 means a 2D layout, dim=3 means a 3D layout.  
Returns  the calculated layout. 
Places the vertices on a 2D plane according to the DavidsonHarel layout algorithm.
The algorithm uses simulated annealing and a sophisticated energy function, which is unfortunately hard to parameterize for different graphs. The original publication did not disclose any parameter values, and the ones below were determined by experimentation.
The algorithm consists of two phases: an annealing phase and a finetuning phase. There is no simulated annealing in the second phase.
Parameters  seed  if None , uses a random starting layout for the algorithm. If a matrix (list of lists), uses the given matrix as the starting position. 
maxiter  Number of iterations to perform in the annealing phase.  
fineiter  Number of iterations to perform in the finetuning phase. Negative numbers set up a reasonable default from the base2 logarithm of the vertex count, bounded by 10 from above.  
cool_fact  Cooling factor of the simulated annealing phase.  
weight_node_dist  Weight for the nodenode distances in the energy function.  
weight_border  Weight for the distance from the border component of the energy function. Zero means that vertices are allowed to sit on the border of the area designated for the layout.  
weight_edge_lengths  Weight for the edge length component of the energy function. Negative numbers are replaced by the density of the graph divided by 10.  
weight_edge_crossings  Weight for the edge crossing component of the energy function. Negative numbers are replaced by one minus the square root of the density of the graph.  
weight_node_edge_dist  Weight for the nodeedge distance component of the energy function. Negative numbers are replaced by 0.2 minus 0.2 times the density of the graph.  
Returns  the calculated layout. 
Places the vertices on a 2D plane or in the 3D space ccording to the DrL layout algorithm.
This is an algorithm suitable for quite large graphs, but it can be surprisingly slow for small ones (where the simpler forcebased layouts like layout_kamada_kawai()
or layout_fruchterman_reingold()
are more useful.
Parameters  weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
fixed  ignored. We used to assume that the DrL layout supports fixed nodes, but later it turned out that the argument has no effect in the original DrL code. We kept the argument for sake of backwards compatibility, but it will have no effect on the final layout.  
seed  if None , uses a random starting layout for the algorithm. If a matrix (list of lists), uses the given matrix as the starting position.  
options  if you give a string argument here, you can select from five default preset parameterisations: default , coarsen for a coarser layout, coarsest for an even coarser layout, refine for refining an existing layout and final for finalizing a layout. If you supply an object that is not a string, the DrL layout parameters are retrieved from the respective keys of the object (so it should be a dict or something else that supports the mapping protocol). The following keys can be used:
Instead of a mapping, you can also use an arbitrary Python object here: if the object does not support the mapping protocol, an attribute of the object with the same name is looked up instead. If a parameter cannot be found either as a key or an attribute, the default from the  
dim  the desired number of dimensions for the layout. dim=2 means a 2D layout, dim=3 means a 3D layout.  
Returns  the calculated layout. 
Places the vertices on a 2D plane according to the FruchtermanReingold algorithm.
This is a force directed layout, see Fruchterman, T. M. J. and Reingold, E. M.: Graph Drawing by Forcedirected Placement. Software  Practice and Experience, 21/11, 11291164, 1991
Parameters  weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
niter  the number of iterations to perform. The default is 500.  
seed  if None , uses a random starting layout for the algorithm. If a matrix (list of lists), uses the given matrix as the starting position.  
start_temp  Real scalar, the start temperature. This is the maximum amount of movement alloved along one axis, within one step, for a vertex. Currently it is decreased linearly to zero during the iteration. The default is the square root of the number of vertices divided by 10.  
minx  if not None , it must be a vector with exactly as many elements as there are vertices in the graph. Each element is a minimum constraint on the X value of the vertex in the layout.  
maxx  similar to minx, but with maximum constraints  
miny  similar to minx, but with the Y coordinates  
maxy  similar to maxx, but with the Y coordinates  
minz  similar to minx, but with the Z coordinates. Use only for 3D layouts (dim =3).  
maxz  similar to maxx, but with the Z coordinates. Use only for 3D layouts (dim =3).  
grid  whether to use a faster, but less accurate gridbased implementation of the algorithm. "auto" decides based on the number of vertices in the graph; a grid will be used if there are at least 1000 vertices. "grid" is equivalent to True , "nogrid" is equivalent to False .  
Returns  the calculated layout. 
This is a port of the graphopt layout algorithm by Michael Schmuhl. graphopt version 0.4.1 was rewritten in C and the support for layers was removed.
graphopt uses physical analogies for defining attracting and repelling forces among the vertices and then the physical system is simulated until it reaches an equilibrium or the maximal number of iterations is reached.
See http://www.schmuhl.org/graphopt/ for the original graphopt.
Parameters  niter  the number of iterations to perform. Should be a couple of hundred in general. 
node_charge  the charge of the vertices, used to calculate electric repulsion.  
node_mass  the mass of the vertices, used for the spring forces  
spring_length  the length of the springs  
spring_constant  the spring constant  
max_sa_movement  the maximum amount of movement allowed in a single step along a single axis.  
seed  a matrix containing a seed layout from which the algorithm will be started. If None , a random layout will be used.  
Returns  the calculated layout. 
Places the vertices on a 2D plane according to the Large Graph Layout.
Parameters  maxiter  the number of iterations to perform. 
maxdelta  the maximum distance to move a vertex in an iteration. If negative, defaults to the number of vertices.  
area  the area of the square on which the vertices will be placed. If negative, defaults to the number of vertices squared.  
coolexp  the cooling exponent of the simulated annealing.  
repulserad  determines the radius at which vertexvertex repulsion cancels out attraction of adjacent vertices. If negative, defaults to area times the number of vertices.  
cellsize  the size of the grid cells. When calculating the repulsion forces, only vertices in the same or neighboring grid cells are taken into account. Defaults to the fourth root of area.  
root  the root vertex, this is placed first, its neighbors in the first iteration, second neighbors in the second, etc. None means that a random vertex will be chosen.  
Returns  the calculated layout. 
Places the vertices in an Euclidean space with the given number of dimensions using multidimensional scaling.
This layout requires a distance matrix, where the intersection of row i and column j specifies the desired distance between vertex i and vertex j. The algorithm will try to place the vertices in a way that approximates the distance relations prescribed in the distance matrix. igraph uses the classical multidimensional scaling by Torgerson (see reference below).
For unconnected graphs, the method will decompose the graph into weakly connected components and then lay out the components individually using the appropriate parts of the distance matrix.
Parameters  dist  the distance matrix. It must be symmetric and the symmetry is not checked  results are unspecified when a nonsymmetric distance matrix is used. If this parameter is None , the shortest path lengths will be used as distances. Directed graphs are treated as undirected when calculating the shortest path lengths to ensure symmetry. 
dim  the number of dimensions. For 2D layouts, supply 2 here; for 3D layouts, supply 3.  
arpack_options  an ARPACKOptions object used to finetune the ARPACK eigenvector calculation. If omitted, the modulelevel variable called arpack_options is used.  
Returns  the calculated layout.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Cox & Cox: Multidimensional Scaling (1994), Chapman and Hall, London. 
Places the vertices on a 2D plane according to the ReingoldTilford layout algorithm.
This is a tree layout. If the given graph is not a tree, a breadthfirst search is executed first to obtain a possible spanning tree.
Parameters  mode  specifies which edges to consider when builing the tree. If it is OUT then only the outgoing, if it is IN then only the incoming edges of a parent are considered. If it is ALL then all edges are used (this was the behaviour in igraph 0.5 and before). This parameter also influences how the root vertices are calculated if they are not given. See the root parameter. 
root  the index of the root vertex or root vertices. if this is a nonempty vector then the supplied vertex IDs are used as the roots of the trees (or a single tree if the graph is connected. If this is None or an empty list, the root vertices are automatically calculated based on topological sorting, performed with the opposite of the mode argument.  
rootlevel  this argument is useful when drawing forests which are not trees. It specifies the level of the root vertices for every tree in the forest.  
Returns  the calculated layout.  
See Also  layout_reingold_tilford_circular  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  EM Reingold, JS Tilford: Tidier Drawings of Trees. IEEE Transactions on Software Engineering 7:22, 223228, 1981. 
Circular ReingoldTilford layout for trees.
This layout is similar to the ReingoldTilford layout, but the vertices are placed in a circular way, with the root vertex in the center.
See layout_reingold_tilford
for the explanation of the parameters.
Returns  the calculated layout.  
See Also  layout_reingold_tilford  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  EM Reingold, JS Tilford: Tidier Drawings of Trees. IEEE Transactions on Software Engineering 7:22, 223228, 1981. 
Places the vertices of the graph randomly.
Parameters  dim  the desired number of dimensions for the layout. dim=2 means a 2D layout, dim=3 means a 3D layout. 
Returns  the coordinate pairs in a list. 
Conducts a breadth first search (BFS) on the graph.
Parameters  vid  the root vertex ID 
mode  either "in" or "out" or "all" , ignored for undirected graphs.  
Returns  a tuple with the following items:

Constructs a breadth first search (BFS) iterator of the graph.
Parameters  vid  the root vertex ID 
mode  either "in" or "out" or "all" .  
advanced  if False , the iterator returns the next vertex in BFS order in every step. If True , the iterator returns the distance of the vertex from the root and the parent of the vertex in the BFS tree as well.  
Returns  the BFS iterator as an igraph.BFSIter object. 
Constructs a depth first search (DFS) iterator of the graph.
Parameters  vid  the root vertex ID 
mode  either "in" or "out" or "all" .  
advanced  if False , the iterator returns the next vertex in DFS order in every step. If True , the iterator returns the distance of the vertex from the root and the parent of the vertex in the DFS tree as well.  
Returns  the DFS iterator as an igraph.DFSIter object. 
igraph.Graph
Returns the adjacency matrix of a graph.
Parameters  type  one of "lower" (uses the lower triangle of the matrix), "upper" (uses the upper triangle) or "both" (uses both parts). Ignored for directed graphs. 
eids  if True , the result matrix will contain zeros for nonedges and the ID of the edge plus one for edges in the appropriate cell. If False , the result matrix will contain the number of edges for each vertex pair.  
Returns  the adjacency matrix. 
igraph.Graph
Internal function, undocumented.
See Also  Graph.get_incidence() 
Converts an undirected graph to directed.
Parameters  mode  specifies how to convert undirected edges into directed ones. True or "mutual" creates a mutual edge pair for each undirected edge. False or "arbitrary" picks an arbitrary (but deterministic) edge direction for each edge. "random" picks a random direction for each edge. "acyclic" picks the edge directions in a way that the resulting graph will be acyclic if there were no selfloops in the original graph. 
Converts a directed graph to undirected.
Parameters  mode  specifies what to do with multiple directed edges going between the same vertex pair. True or "collapse" means that only a single edge should be created from multiple directed edges. False or "each" means that every edge will be kept (with the arrowheads removed). "mutual" creates one undirected edge for each mutual directed edge pair. 
combine_edges  specifies how to combine the attributes of multiple edges between the same pair of vertices into a single attribute. See simplify() for more details. 
Returns the Laplacian matrix of a graph.
The Laplacian matrix is similar to the adjacency matrix, but the edges are denoted with 1 and the diagonal contains the node degrees.
Normalized Laplacian matrices have 1 or 0 in their diagonals (0 for vertices with no edges), edges are denoted by 1 / sqrt(d_i * d_j) where d_i is the degree of node i.
Multiple edges and selfloops are silently ignored. Although it is possible to calculate the Laplacian matrix of a directed graph, it does not make much sense.
Parameters  weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. When edge weights are used, the degree of a node is considered to be the weight of its incident edges. 
normalized  whether to return the normalized Laplacian matrix.  
Returns  the Laplacian matrix. 
Reads a graph from a file conforming to the DIMACS minimumcost flow file format.
For the exact description of the format, see http://lpsolve.sourceforge.net/5.5/DIMACS.htm
Restrictions compared to the official description of the format:
Parameters  f  the name of the file or a Python file handle 
directed  whether the generated graph should be directed.  
Returns  the generated graph, the source and the target of the flow and the edge capacities in a tuple 
Reads an UCINET DL file and creates a graph based on it.
Parameters  f  the name of the file or a Python file handle 
directed  whether the generated graph should be directed. 
Reads an edge list from a file and creates a graph based on it.
Please note that the vertex indices are zerobased. A vertex of zero degree will be created for every integer that is in range but does not appear in the edgelist.
Parameters  f  the name of the file or a Python file handle 
directed  whether the generated graph should be directed. 
Reads a GraphDB format file and creates a graph based on it.
GraphDB is a binary format, used in the graph database for isomorphism testing (see http://amalfi.dis.unina.it/graph/).
Parameters  f  the name of the file or a Python file handle 
directed  whether the generated graph should be directed. 
Reads a GraphML format file and creates a graph based on it.
Parameters  f  the name of the file or a Python file handle 
directed  Undocumented  
index  if the GraphML file contains multiple graphs, specifies the one that should be loaded. Graph indices start from zero, so if you want to load the first graph, specify 0 here. 
Reads a GML file and creates a graph based on it.
Parameters  f  the name of the file or a Python file handle 
Reads an .ncol file used by LGL.
It is also useful for creating graphs from "named" (and optionally weighted) edge lists.
This format is used by the Large Graph Layout program. See the repository of LGL for more information.
LGL originally cannot deal with graphs containing multiple or loop edges, but this condition is not checked here, as igraph is happy with these.
Parameters  f  the name of the file or a Python file handle 
names  If True , the vertex names are added as a vertex attribute called 'name'.  
weights  If True, the edge weights are added as an edge attribute called 'weight', even if there are no weights in the file. If False, the edge weights are never added, even if they are present. "auto" or "if_present" means that weights are added if there is at least one weighted edge in the input file, but they are not added otherwise.  
directed  whether the graph being created should be directed 
Reads an .lgl file used by LGL.
It is also useful for creating graphs from "named" (and optionally weighted) edge lists.
This format is used by the Large Graph Layout program. See the documentation of LGL regarding the exact format description.
LGL originally cannot deal with graphs containing multiple or loop edges, but this condition is not checked here, as igraph is happy with these.
Parameters  f  the name of the file or a Python file handle 
names  If True , the vertex names are added as a vertex attribute called 'name'.  
weights  If True, the edge weights are added as an edge attribute called 'weight', even if there are no weights in the file. If False, the edge weights are never added, even if they are present. "auto" or "if_present" means that weights are added if there is at least one weighted edge in the input file, but they are not added otherwise.  
directed  whether the graph being created should be directed 
Reads a Pajek format file and creates a graph based on it.
Parameters  f  the name of the file or a Python file handle 
Writes the graph in DIMACS format to the given file.
Parameters  f  the name of the file to be written or a Python file handle 
source  the source vertex ID  
target  the target vertex ID  
capacity  the capacities of the edges in a list. If it is not a list, the corresponding edge attribute will be used to retrieve capacities. 
Writes the graph in DOT format to the given file.
DOT is the format used by the GraphViz software package.
Parameters  f  the name of the file to be written or a Python file handle 
Writes the edge list of a graph to a file.
Directed edges are written in (from, to) order.
Parameters  f  the name of the file to be written or a Python file handle 
Writes the graph in GML format to the given file.
Parameters  f  the name of the file to be written or a Python file handle 
creator  optional creator information to be written to the file. If None , the current date and time is added.  
ids  optional numeric vertex IDs to use in the file. This must be a list of integers or None . If None , the id attribute of the vertices are used, or if they don't exist, numeric vertex IDs will be generated automatically. 
Writes the edge list of a graph to a file in .ncol format.
Note that multiple edges and/or loops break the LGL software, but igraph does not check for this condition. Unless you know that the graph does not have multiple edges and/or loops, it is wise to call simplify()
before saving.
Parameters  f  the name of the file to be written or a Python file handle 
names  the name of the vertex attribute containing the name of the vertices. If you don't want to store vertex names, supply None here.  
weights  the name of the edge attribute containing the weight of the vertices. If you don't want to store weights, supply None here. 
Writes the edge list of a graph to a file in .lgl format.
Note that multiple edges and/or loops break the LGL software, but igraph does not check for this condition. Unless you know that the graph does not have multiple edges and/or loops, it is wise to call simplify()
before saving.
Parameters  f  the name of the file to be written or a Python file handle 
names  the name of the vertex attribute containing the name of the vertices. If you don't want to store vertex names, supply None here.  
weights  the name of the edge attribute containing the weight of the vertices. If you don't want to store weights, supply None here.  
isolates  whether to include isolated vertices in the output. 
Writes the graph in Pajek format to the given file.
Parameters  f  the name of the file to be written or a Python file handle 
Writes the graph to a GraphML file.
Parameters  f  the name of the file to be written or a Python file handle 
Writes the graph to a file in LEDA native format.
The LEDA format supports at most one attribute per vertex and edge. You can specify which vertex and edge attribute you want to use. Note that the name of the attribute is not saved in the LEDA file.
Parameters  f  the name of the file to be written or a Python file handle 
names  the name of the vertex attribute to be stored along with the vertices. It is usually used to store the vertex names (hence the name of the keyword argument), but you may also use a numeric attribute. If you don't want to store any vertex attributes, supply None here.  
weights  the name of the edge attribute to be stored along with the edges. It is usually used to store the edge weights (hence the name of the keyword argument), but you may also use a string attribute. If you don't want to store any edge attributes, supply None here. 
Calculates the canonical permutation of a graph using the BLISS isomorphism algorithm.
Passing the permutation returned here to permute_vertices()
will transform the graph into its canonical form.
See http://www.tcs.hut.fi/Software/bliss/index.html for more information about the BLISS algorithm and canonical permutations.
Parameters  sh  splitting heuristics for graph as a caseinsensitive string, with the following possible values:

color  optional vector storing a coloring of the vertices with respect to which the isomorphism is computed.If None , all vertices have the same color.  
Returns  a permutation vector containing vertex IDs. Vertex 0 in the original graph will be mapped to an ID contained in the first element of this vector; vertex 1 will be mapped to the second and so on. 
Returns the isomorphism class of the graph or its subgraph.
Isomorphy class calculations are implemented only for graphs with 3 or 4 vertices.
Parameters  vertices  a list of vertices if we want to calculate the isomorphism class for only a subset of vertices. None means to use the full graph. 
Returns  the isomorphism class of the (sub)graph 
Checks whether the graph is isomorphic to another graph.
The algorithm being used is selected using a simple heuristic:
False
isomorphic_vf2
).isomorphic_bliss
.Returns  True if the graphs are isomorphic, False otherwise. 
Checks whether the graph is isomorphic to another graph, using the BLISS isomorphism algorithm.
See http://www.tcs.hut.fi/Software/bliss/index.html for more information about the BLISS algorithm.
Parameters  other  the other graph with which we want to compare the graph. 
return_mapping_12  if True , calculates the mapping which maps the vertices of the first graph to the second.  
return_mapping_21  if True , calculates the mapping which maps the vertices of the second graph to the first.  
sh1  splitting heuristics for the first graph as a caseinsensitive string, with the following possible values:
 
sh2  splitting heuristics to be used for the second graph. This must be the same as sh1 ; alternatively, it can be None , in which case it will automatically use the same value as sh1 . Currently it is present for backwards compatibility only.  
color1  optional vector storing the coloring of the vertices of the first graph. If None , all vertices have the same color.  
color2  optional vector storing the coloring of the vertices of the second graph. If None , all vertices have the same color.  
Returns  if no mapping is calculated, the result is True if the graphs are isomorphic, False otherwise. If any or both mappings are calculated, the result is a 3tuple, the first element being the above mentioned boolean, the second element being the 1 > 2 mapping and the third element being the 2 > 1 mapping. If the corresponding mapping was not calculated, None is returned in the appropriate element of the 3tuple. 
Checks whether the graph is isomorphic to another graph, using the VF2 isomorphism algorithm.
Vertex and edge colors may be used to restrict the isomorphisms, as only vertices and edges with the same color will be allowed to match each other.
Parameters  other  the other graph with which we want to compare the graph. If None , the automorphjisms of the graph will be tested. 
color1  optional vector storing the coloring of the vertices of the first graph. If None , all vertices have the same color.  
color2  optional vector storing the coloring of the vertices of the second graph. If None , all vertices have the same color.  
edge_color1  optional vector storing the coloring of the edges of the first graph. If None , all edges have the same color.  
edge_color2  optional vector storing the coloring of the edges of the second graph. If None , all edges have the same color.  
return_mapping_12  if True , calculates the mapping which maps the vertices of the first graph to the second.  
return_mapping_21  if True , calculates the mapping which maps the vertices of the second graph to the first.  
node_compat_fn  a function that receives the two graphs and two node indices (one from the first graph, one from the second graph) and returns True if the nodes given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on nodespecific criteria that are too complicated to be represented by node color vectors (i.e. the color1 and color2 parameters). None means that every node is compatible with every other node.  
edge_compat_fn  a function that receives the two graphs and two edge indices (one from the first graph, one from the second graph) and returns True if the edges given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on edgespecific criteria that are too complicated to be represented by edge color vectors (i.e. the edge_color1 and edge_color2 parameters). None means that every edge is compatible with every other node.  
callback  if not None , the isomorphism search will not stop at the first match; it will call this callback function instead for every isomorphism found. The callback function must accept four arguments: the first graph, the second graph, a mapping from the nodes of the first graph to the second, and a mapping from the nodes of the second graph to the first. The function must return True if the search should continue or False otherwise.  
Returns  if no mapping is calculated, the result is True if the graphs are isomorphic, False otherwise. If any or both mappings are calculated, the result is a 3tuple, the first element being the above mentioned boolean, the second element being the 1 > 2 mapping and the third element being the 2 > 1 mapping. If the corresponding mapping was not calculated, None is returned in the appropriate element of the 3tuple. 
Determines the number of isomorphisms between the graph and another one
Vertex and edge colors may be used to restrict the isomorphisms, as only vertices and edges with the same color will be allowed to match each other.
Parameters  other  the other graph. If None , the number of automorphisms will be returned. 
color1  optional vector storing the coloring of the vertices of the first graph. If None , all vertices have the same color.  
color2  optional vector storing the coloring of the vertices of the second graph. If None , all vertices have the same color.  
edge_color1  optional vector storing the coloring of the edges of the first graph. If None , all edges have the same color.  
edge_color2  optional vector storing the coloring of the edges of the second graph. If None , all edges have the same color.  
node_compat_fn  a function that receives the two graphs and two node indices (one from the first graph, one from the second graph) and returns True if the nodes given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on nodespecific criteria that are too complicated to be represented by node color vectors (i.e. the color1 and color2 parameters). None means that every node is compatible with every other node.  
edge_compat_fn  a function that receives the two graphs and two edge indices (one from the first graph, one from the second graph) and returns True if the edges given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on edgespecific criteria that are too complicated to be represented by edge color vectors (i.e. the edge_color1 and edge_color2 parameters). None means that every edge is compatible with every other node.  
Returns  the number of isomorphisms between the two given graphs (or the number of automorphisms if other is None . 
Returns all isomorphisms between the graph and another one
Vertex and edge colors may be used to restrict the isomorphisms, as only vertices and edges with the same color will be allowed to match each other.
Parameters  other  the other graph. If None , the automorphisms will be returned. 
color1  optional vector storing the coloring of the vertices of the first graph. If None , all vertices have the same color.  
color2  optional vector storing the coloring of the vertices of the second graph. If None , all vertices have the same color.  
edge_color1  optional vector storing the coloring of the edges of the first graph. If None , all edges have the same color.  
edge_color2  optional vector storing the coloring of the edges of the second graph. If None , all edges have the same color.  
node_compat_fn  a function that receives the two graphs and two node indices (one from the first graph, one from the second graph) and returns True if the nodes given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on nodespecific criteria that are too complicated to be represented by node color vectors (i.e. the color1 and color2 parameters). None means that every node is compatible with every other node.  
edge_compat_fn  a function that receives the two graphs and two edge indices (one from the first graph, one from the second graph) and returns True if the edges given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on edgespecific criteria that are too complicated to be represented by edge color vectors (i.e. the edge_color1 and edge_color2 parameters). None means that every edge is compatible with every other node.  
Returns  a list of lists, each item of the list containing the mapping from vertices of the second graph to the vertices of the first one 
Checks whether a subgraph of the graph is isomorphic to another graph.
Vertex and edge colors may be used to restrict the isomorphisms, as only vertices and edges with the same color will be allowed to match each other.
Parameters  other  the other graph with which we want to compare the graph. 
color1  optional vector storing the coloring of the vertices of the first graph. If None , all vertices have the same color.  
color2  optional vector storing the coloring of the vertices of the second graph. If None , all vertices have the same color.  
edge_color1  optional vector storing the coloring of the edges of the first graph. If None , all edges have the same color.  
edge_color2  optional vector storing the coloring of the edges of the second graph. If None , all edges have the same color.  
return_mapping_12  if True , calculates the mapping which maps the vertices of the first graph to the second. The mapping can contain 1 if a given node is not mapped.  
return_mapping_21  if True , calculates the mapping which maps the vertices of the second graph to the first. The mapping can contain 1 if a given node is not mapped.  
callback  if not None , the subisomorphism search will not stop at the first match; it will call this callback function instead for every subisomorphism found. The callback function must accept four arguments: the first graph, the second graph, a mapping from the nodes of the first graph to the second, and a mapping from the nodes of the second graph to the first. The function must return True if the search should continue or False otherwise.  
node_compat_fn  a function that receives the two graphs and two node indices (one from the first graph, one from the second graph) and returns True if the nodes given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on nodespecific criteria that are too complicated to be represented by node color vectors (i.e. the color1 and color2 parameters). None means that every node is compatible with every other node.  
edge_compat_fn  a function that receives the two graphs and two edge indices (one from the first graph, one from the second graph) and returns True if the edges given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on edgespecific criteria that are too complicated to be represented by edge color vectors (i.e. the edge_color1 and edge_color2 parameters). None means that every edge is compatible with every other node.  
Returns  if no mapping is calculated, the result is True if the graph contains a subgraph that's isomorphic to the given one, False otherwise. If any or both mappings are calculated, the result is a 3tuple, the first element being the above mentioned boolean, the second element being the 1 > 2 mapping and the third element being the 2 > 1 mapping. If the corresponding mapping was not calculated, None is returned in the appropriate element of the 3tuple. 
Determines the number of subisomorphisms between the graph and another one
Vertex and edge colors may be used to restrict the isomorphisms, as only vertices and edges with the same color will be allowed to match each other.
Parameters  other  the other graph. 
color1  optional vector storing the coloring of the vertices of the first graph. If None , all vertices have the same color.  
color2  optional vector storing the coloring of the vertices of the second graph. If None , all vertices have the same color.  
edge_color1  optional vector storing the coloring of the edges of the first graph. If None , all edges have the same color.  
edge_color2  optional vector storing the coloring of the edges of the second graph. If None , all edges have the same color.  
node_compat_fn  a function that receives the two graphs and two node indices (one from the first graph, one from the second graph) and returns True if the nodes given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on nodespecific criteria that are too complicated to be represented by node color vectors (i.e. the color1 and color2 parameters). None means that every node is compatible with every other node.  
edge_compat_fn  a function that receives the two graphs and two edge indices (one from the first graph, one from the second graph) and returns True if the edges given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on edgespecific criteria that are too complicated to be represented by edge color vectors (i.e. the edge_color1 and edge_color2 parameters). None means that every edge is compatible with every other node.  
Returns  the number of subisomorphisms between the two given graphs 
Returns all subisomorphisms between the graph and another one
Vertex and edge colors may be used to restrict the isomorphisms, as only vertices and edges with the same color will be allowed to match each other.
Parameters  other  the other graph. 
color1  optional vector storing the coloring of the vertices of the first graph. If None , all vertices have the same color.  
color2  optional vector storing the coloring of the vertices of the second graph. If None , all vertices have the same color.  
edge_color1  optional vector storing the coloring of the edges of the first graph. If None , all edges have the same color.  
edge_color2  optional vector storing the coloring of the edges of the second graph. If None , all edges have the same color.  
node_compat_fn  a function that receives the two graphs and two node indices (one from the first graph, one from the second graph) and returns True if the nodes given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on nodespecific criteria that are too complicated to be represented by node color vectors (i.e. the color1 and color2 parameters). None means that every node is compatible with every other node.  
edge_compat_fn  a function that receives the two graphs and two edge indices (one from the first graph, one from the second graph) and returns True if the edges given by the two indices are compatible (i.e. they could be matched to each other) or False otherwise. This can be used to restrict the set of isomorphisms based on edgespecific criteria that are too complicated to be represented by edge color vectors (i.e. the edge_color1 and edge_color2 parameters). None means that every edge is compatible with every other node.  
Returns  a list of lists, each item of the list containing the mapping from vertices of the second graph to the vertices of the first one 
Checks whether a subgraph of the graph is isomorphic to another graph.
The optional domains
argument may be used to restrict vertices that may match each other. You can also specify whether you are interested in induced subgraphs only or not.
Parameters  other  the pattern graph we are looking for in the graph. 
domains  a list of lists, one sublist belonging to each vertex in the template graph. Sublist i contains the indices of the vertices in the original graph that may match vertex i in the template graph. None means that every vertex may match every other vertex.  
induced  whether to consider induced subgraphs only.  
time_limit  an optimal time limit in seconds. Only the integral part of this number is taken into account. If the time limit is exceeded, the method will throw an exception.  
return_mapping  when True , the function will return a tuple, where the first element is a boolean denoting whether a subisomorphism has been found or not, and the second element describes the mapping of the vertices from the template graph to the original graph. When False , only the boolean is returned.  
Returns  if no mapping is calculated, the result is True if the graph contains a subgraph that is isomorphic to the given template, False otherwise. If the mapping is calculated, the result is a tuple, the first element being the above mentioned boolean, and the second element being the mapping from the target to the original graph. 
Returns all subisomorphisms between the graph and another one using the LAD algorithm.
The optional domains
argument may be used to restrict vertices that may match each other. You can also specify whether you are interested in induced subgraphs only or not.
Parameters  other  the pattern graph we are looking for in the graph. 
domains  a list of lists, one sublist belonging to each vertex in the template graph. Sublist i contains the indices of the vertices in the original graph that may match vertex i in the template graph. None means that every vertex may match every other vertex.  
induced  whether to consider induced subgraphs only.  
time_limit  an optimal time limit in seconds. Only the integral part of this number is taken into account. If the time limit is exceeded, the method will throw an exception.  
Returns  a list of lists, each item of the list containing the mapping from vertices of the second graph to the vertices of the first one 
Returns the complementer of the graph
Parameters  loops  whether to include loop edges in the complementer. 
Returns  the complementer of the graph 
Returns the dominator tree from the given root node
Parameters  vid  the root vertex ID 
mode  either "in" or "out"  
Returns  a list containing the dominator tree for the current graph. 
Returns the value of the maximum flow between the source and target vertices.
Parameters  source  the source vertex ID 
target  the target vertex ID  
capacity  the capacity of the edges. It must be a list or a valid attribute name or None . In the latter case, every edge will have the same capacity.  
Returns  the value of the maximum flow between the given vertices 
igraph.Graph
Returns the maximum flow between the source and target vertices.
Parameters  source  the source vertex ID 
target  the target vertex ID  
capacity  the capacity of the edges. It must be a list or a valid attribute name or None . In the latter case, every edge will have the same capacity.  
Returns  a tuple containing the following: the value of the maximum flow between the given vertices, the flow value on all the edges, the edge IDs that are part of the corresponding minimum cut, and the vertex IDs on one side of the cut. For directed graphs, the flow value vector gives the flow value on each edge. For undirected graphs, the flow value is positive if the flow goes from the smaller vertex ID to the bigger one and negative if the flow goes from the bigger vertex ID to the smaller.  
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a Flow object. It is advised to use that. 
igraph.Graph
Returns all the cuts between the source and target vertices in a directed graph.
This function lists all edgecuts between a source and a target vertex. Every cut is listed exactly once.
Parameters  source  the source vertex ID 
target  the target vertex ID  
Returns  a tuple where the first element is a list of lists of edge IDs representing a cut and the second element is a list of lists of vertex IDs representing the sets of vertices that were separated by the cuts.  
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a list of Cut objects. It is advised to use that. 
igraph.Graph
Returns all minimum cuts between the source and target vertices in a directed graph.
Parameters  source  the source vertex ID 
target  the target vertex ID  
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a list of Cut objects. It is advised to use that. 
Returns the minimum cut between the source and target vertices or within the whole graph.
Parameters  source  the source vertex ID. If negative, the calculation is done for every vertex except the target and the minimum is returned. 
target  the target vertex ID. If negative, the calculation is done for every vertex except the source and the minimum is returned.  
capacity  the capacity of the edges. It must be a list or a valid attribute name or None . In the latter case, every edge will have the same capacity.  
Returns  the value of the minimum cut between the given vertices 
igraph.Graph
Calculates the minimum cut between the source and target vertices or within the whole graph.
The minimum cut is the minimum set of edges that needs to be removed to separate the source and the target (if they are given) or to disconnect the graph (if the source and target are not given). The minimum is calculated using the weights (capacities) of the edges, so the cut with the minimum total capacity is calculated. For undirected graphs and no source and target, the method uses the StoerWagner algorithm. For a given source and target, the method uses the pushrelabel algorithm; see the references below.
Parameters  source  the source vertex ID. If None , target must also be {None} and the calculation will be done for the entire graph (i.e. all possible vertex pairs). 
target  the target vertex ID. If None , source must also be {None} and the calculation will be done for the entire graph (i.e. all possible vertex pairs).  
capacity  the capacity of the edges. It must be a list or a valid attribute name or None . In the latter case, every edge will have the same capacity.  
Returns  the value of the minimum cut, the IDs of vertices in the first and second partition, and the IDs of edges in the cut, packed in a 4tuple  
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a Cut object. It is advised to use that.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  M. Stoer, F. Wagner: A simple mincut algorithm. Journal of the ACM 44(4):585591, 1997.  
A. V. Goldberg, R. E. Tarjan: A new approach to the maximumflow problem. Journal of the ACM 35(4):921940, 1988. 
igraph.Graph
Calculates the minimum cut between the source and target vertices in a graph.
Parameters  source  the source vertex ID 
target  the target vertex ID  
capacity  the capacity of the edges. It must be a list or a valid attribute name or None . In the latter case, every edge will have the same capacity.  
Returns  the value of the minimum cut, the IDs of vertices in the first and second partition, and the IDs of edges in the cut, packed in a 4tuple  
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a list of Cut objects. It is advised to use that. 
igraph.Graph
Internal function, undocumented.
See Also  Graph.gomory_hu_tree() 
Returns a list containing all the minimal st separators of a graph.
A minimal separator is a set of vertices whose removal disconnects the graph, while the removal of any subset of the set keeps the graph connected.
Returns  a list where each item lists the vertex indices of a given minimal st separator.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Anne Berry, JeanPaul Bordat and Olivier Cogis: Generating all the minimal separators of a graph. In: Peter Widmayer, Gabriele Neyer and Stephan Eidenbenz (eds.): Graphtheoretic concepts in computer science, 1665, 167172, 1999. Springer. 
Decides whether the given vertex set is a minimal separator.
A minimal separator is a set of vertices whose removal disconnects the graph, while the removal of any subset of the set keeps the graph connected.
Parameters  vertices  a single vertex ID or a list of vertex IDs 
Returns  True is the given vertex set is a minimal separator, False otherwise. 
Decides whether the removal of the given vertices disconnects the graph.
Parameters  vertices  a single vertex ID or a list of vertex IDs 
Returns  True is the given vertex set is a separator, False if not. 
Returns a list containing all separator vertex sets of minimum size.
A vertex set is a separator if its removal disconnects the graph. This method lists all the separators for which no smaller separator set exists in the given graph.
Returns  a list where each item lists the vertex indices of a given separator of minimum size.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Arkady Kanevsky: Finding all minimumsize separating vertex sets in a graph. Networks 23:533541, 1993. 
igraph.Graph
Calculates the cohesive block structure of the graph.
Unknown Field: attention  this function has a more convenient interface in class Graph which wraps the result in a CohesiveBlocks object. It is advised to use that. 
Returns some or all cliques of the graph as a list of tuples.
A clique is a complete subgraph  a set of vertices where an edge is present between any two of them (excluding loops)
Parameters  min  the minimum size of cliques to be returned. If zero or negative, no lower bound will be used. 
max  the maximum size of cliques to be returned. If zero or negative, no upper bound will be used. 
Returns the largest cliques of the graph as a list of tuples.
Quite intuitively a clique is considered largest if there is no clique with more vertices in the whole graph. All largest cliques are maximal (i.e. nonextendable) but not all maximal cliques are largest.
See Also  clique_number() for the size of the largest cliques or maximal_cliques() for the maximal cliques 
Returns the maximal cliques of the graph as a list of tuples.
A maximal clique is a clique which can't be extended by adding any other vertex to it. A maximal clique is not necessarily one of the largest cliques in the graph.
Parameters  min  the minimum size of maximal cliques to be returned. If zero or negative, no lower bound will be used. 
max  the maximum size of maximal cliques to be returned. If zero or negative, no upper bound will be used. If nonzero, the size of every maximal clique found will be compared to this value and a clique will be returned only if its size is smaller than this limit.  
file  a file object or the name of the file to write the results to. When this argument is None , the maximal cliques will be returned as a list of lists.  
Returns  the maximal cliques of the graph as a list of lists, or None if the file argument was given.@see: largest_cliques() for the largest cliques. 
Returns the clique number of the graph.
The clique number of the graph is the size of the largest clique.
See Also  largest_cliques() for the largest cliques. 
Returns some or all independent vertex sets of the graph as a list of tuples.
Two vertices are independent if there is no edge between them. Members of an independent vertex set are mutually independent.
Parameters  min  the minimum size of sets to be returned. If zero or negative, no lower bound will be used. 
max  the maximum size of sets to be returned. If zero or negative, no upper bound will be used. 
Returns the largest independent vertex sets of the graph as a list of tuples.
Quite intuitively an independent vertex set is considered largest if there is no other set with more vertices in the whole graph. All largest sets are maximal (i.e. nonextendable) but not all maximal sets are largest.
See Also  independence_number() for the size of the largest independent vertex sets or maximal_independent_vertex_sets() for the maximal (nonextendable) independent vertex sets 
Returns the maximal independent vertex sets of the graph as a list of tuples.
A maximal independent vertex set is an independent vertex set which can't be extended by adding any other vertex to it. A maximal independent vertex set is not necessarily one of the largest independent vertex sets in the graph.
See Also  largest_independent_vertex_sets() for the largest independent vertex sets  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka: A new algorithm for generating all the maximal independent sets. SIAM J Computing, 6:505517, 1977. 
Returns the independence number of the graph.
The independence number of the graph is the size of the largest independent vertex set.
See Also  largest_independent_vertex_sets() for the largest independent vertex sets 
igraph.Graph
Calculates the modularity of the graph with respect to some vertex types.
The modularity of a graph w.r.t. some division measures how good the division is, or how separated are the different vertex types from each other. It is defined as Q=1/(2m) * sum(Aijgamma*ki*kj/(2m)delta(ci,cj),i,j). m is the number of edges, Aij is the element of the A adjacency matrix in row i and column j, ki is the degree of node i, kj is the degree of node j, Ci and cj
are the types of the two vertices (i and j), and gamma is a resolution parameter that defaults to 1 for the classical definition of modularity. delta(x,y) is one iff x=y, 0 otherwise.
If edge weights are given, the definition of modularity is modified as follows: Aij becomes the weight of the corresponding edge, ki is the total weight of edges incident on vertex i, kj is the total weight of edges incident on vertex j and m is the total edge weight in the graph.
Parameters  membership  the membership vector, e.g. the vertex type index for each vertex. 
weights  optional edge weights or None if all edges are weighed equally.  
resolution  the resolution parameter gamma in the formula above. The classical definition of modularity is retrieved when the resolution parameter is set to 1.  
directed  whether to consider edge directions if the graph is directed. True will use the directed variant of the modularity measure where the in and outdegrees of nodes are treated separately; False will treat directed graphs as undirected.  
Returns  the modularity score. Score larger than 0.3 usually indicates strong community structure.  
Unknown Field: attention  method overridden in Graph to allow VertexClustering objects as a parameter. This method is not strictly necessary, since the VertexClustering class provides a variable called modularity .  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  MEJ Newman and M Girvan: Finding and evaluating community structure in networks. Phys Rev E 69 026113, 2004. 
Finds the coreness (shell index) of the vertices of the network.
The kcore of a graph is a maximal subgraph in which each vertex has at least degree k. (Degree here means the degree in the subgraph of course). The coreness of a vertex is k if it is a member of the kcore but not a member of the k+1core.
Parameters  mode  whether to compute the incorenesses ("in" ), the outcorenesses ("out" ) or the undirected corenesses ("all" ). Ignored and assumed to be "all" for undirected graphs. 
Returns  the corenesses for each vertex.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Vladimir Batagelj, Matjaz Zaversnik: An O(m) Algorithm for Core Decomposition of Networks. 
igraph.Graph
Finds the community structure of the graph according to the algorithm of Clauset et al based on the greedy optimization of modularity.
This is a bottomup algorithm: initially every vertex belongs to a separate community, and communities are merged one by one. In every step, the two communities being merged are the ones which result in the maximal increase in modularity.
Parameters  weights  name of an edge attribute or a list containing edge weights 
Returns  a tuple with the following elements:
 
See Also  modularity()  
Unknown Field: attention  this function is wrapped in a more convenient syntax in the derived class Graph . It is advised to use that instead of this version.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  A. Clauset, M. E. J. Newman and C. Moore: Finding community structure in very large networks. Phys Rev E 70, 066111 (2004). 
igraph.Graph
Finds the community structure of the network according to the Infomap method of Martin Rosvall and Carl T. Bergstrom.
See http://www.mapequation.org for a visualization of the algorithm or one of the references provided below.
Parameters  edge_weights  name of an edge attribute or a list containing edge weights. 
vertex_weights  name of an vertex attribute or a list containing vertex weights.  
trials  the number of attempts to partition the network.  
Returns  the calculated membership vector and the corresponding codelength in a tuple.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  M. Rosvall and C. T. Bergstrom: Maps of information flow reveal community structure in complex networks. PNAS 105, 1118 (2008). http://arxiv.org/abs/0707.0609  
M. Rosvall, D. Axelsson and C. T. Bergstrom: The map equation. Eur Phys J Special Topics 178, 13 (2009). http://arxiv.org/abs/0906.1405 
igraph.Graph
Finds the community structure of the graph according to the label propagation method of Raghavan et al.
Initially, each vertex is assigned a different label. After that, each vertex chooses the dominant label in its neighbourhood in each iteration. Ties are broken randomly and the order in which the vertices are updated is randomized before every iteration. The algorithm ends when vertices reach a consensus.
Note that since ties are broken randomly, there is no guarantee that the algorithm returns the same community structure after each run. In fact, they frequently differ. See the paper of Raghavan et al on how to come up with an aggregated community structure.
Parameters  weights  name of an edge attribute or a list containing edge weights 
initial  name of a vertex attribute or a list containing the initial vertex labels. Labels are identified by integers from zero to n1 where n is the number of vertices. Negative numbers may also be present in this vector, they represent unlabeled vertices.  
fixed  a list of booleans for each vertex. True corresponds to vertices whose labeling should not change during the algorithm. It only makes sense if initial labels are also given. Unlabeled vertices cannot be fixed. Note that vertex attribute names are not accepted here.  
Returns  the resulting membership vector  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Raghavan, U.N. and Albert, R. and Kumara, S. Near linear time algorithm to detect community structures in largescale networks. Phys Rev E 76:036106, 2007. http://arxiv.org/abs/0709.2938. 
igraph.Graph
A proper implementation of Newman's eigenvector community structure detection. Each split is done by maximizing the modularity regarding the original network. See the reference for details.
Parameters  n  the desired number of communities. If negative, the algorithm tries to do as many splits as possible. Note that the algorithm won't split a community further if the signs of the leading eigenvector are all the same. 
arpack_options  an ARPACKOptions object used to finetune the ARPACK eigenvector calculation. If omitted, the modulelevel variable called arpack_options is used.  
weights  name of an edge attribute or a list containing edge weights  
Returns  a tuple where the first element is the membership vector of the clustering and the second element is the merge matrix.  
Unknown Field: attention  this function is wrapped in a more convenient syntax in the derived class Graph . It is advised to use that instead of this version.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  MEJ Newman: Finding community structure in networks using the eigenvectors of matrices, arXiv:physics/0605087 
igraph.Graph
Finds the community structure of the graph according to the multilevel algorithm of Blondel et al. This is a bottomup algorithm: initially every vertex belongs to a separate community, and vertices are moved between communities iteratively in a way that maximizes the vertices' local contribution to the overall modularity score. When a consensus is reached (i.e. no single move would increase the modularity score), every community in the original graph is shrank to a single vertex (while keeping the total weight of the incident edges) and the process continues on the next level. The algorithm stops when it is not possible to increase the modularity any more after shrinking the communities to vertices.
Parameters  weights  name of an edge attribute or a list containing edge weights 
return_levels  if True , returns the multilevel result. If False , only the best level (corresponding to the best modularity) is returned.  
resolution  the resolution parameter to use in the modularity measure. Smaller values result in a smaller number of larger clusters, while higher values yield a large number of small clusters. The classical modularity measure assumes a resolution parameter of 1.  
Returns  either a single list describing the community membership of each vertex (if return_levels is False ), or a list of community membership vectors, one corresponding to each level and a list of corresponding modularities (if return_levels is True ).  
See Also  modularity()  
Unknown Field: attention  this function is wrapped in a more convenient syntax in the derived class Graph . It is advised to use that instead of this version.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  VD Blondel, JL Guillaume, R Lambiotte and E Lefebvre: Fast unfolding of community hierarchies in large networks. J Stat Mech P10008 (2008), http://arxiv.org/abs/0803.0476 
igraph.Graph
Community structure detection based on the betweenness of the edges in the network. This algorithm was invented by M Girvan and MEJ Newman, see: M Girvan and MEJ Newman: Community structure in social and biological networks, Proc. Nat. Acad. Sci. USA 99, 78217826 (2002).
The idea is that the betweenness of the edges connecting two communities is typically high. So we gradually remove the edge with the highest betweenness from the network and recalculate edge betweenness after every removal, as long as all edges are removed.
Parameters  directed  whether to take into account the directedness of the edges when we calculate the betweenness values. 
weights  name of an edge attribute or a list containing edge weights.  
Returns  a tuple with the merge matrix that describes the dendrogram and the modularity scores before each merge. The modularity scores use the weights if the original graph was weighted.  
Unknown Field: attention  this function is wrapped in a more convenient syntax in the derived class Graph . It is advised to use that instead of this version. 
igraph.Graph
Calculates the optimal modularity score of the graph and the corresponding community structure.
This function uses the GNU Linear Programming Kit to solve a large integer optimization problem in order to find the optimal modularity score and the corresponding community structure, therefore it is unlikely to work for graphs larger than a few (less than a hundred) vertices. Consider using one of the heuristic approaches instead if you have such a large graph.
Parameters  weights  name of an edge attribute or a list containing edge weights. 
Returns  the calculated membership vector and the corresponding modularity in a tuple. 
igraph.Graph
Finds the community structure of the graph according to the spinglass community detection method of Reichardt & Bornholdt.
Parameters  weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
spins  integer, the number of spins to use. This is the upper limit for the number of communities. It is not a problem to supply a (reasonably) big number here, in which case some spin states will be unpopulated.  
parupdate  whether to update the spins of the vertices in parallel (synchronously) or not  
start_temp  the starting temperature  
stop_temp  the stop temperature  
cool_fact  cooling factor for the simulated annealing  
update_rule  specifies the null model of the simulation. Possible values are "config" (a random graph with the same vertex degrees as the input graph) or "simple" (a random graph with the same number of edges)  
gamma  the gamma argument of the algorithm, specifying the balance between the importance of present and missing edges within a community. The default value of 1.0 assigns equal importance to both of them.  
implementation  currently igraph contains two implementations for the spinglass community detection algorithm. The faster original implementation is the default. The other implementation is able to take into account negative weights, this can be chosen by setting implementation to "neg" .  
lambda_  the lambda argument of the algorithm, which specifies the balance between the importance of present and missing negatively weighted edges within a community. Smaller values of lambda lead to communities with less negative intraconnectivity. If the argument is zero, the algorithm reduces to a graph coloring algorithm, using the number of spins as colors. This argument is ignored if the original implementation is used.  
Returns  the community membership vector. 
igraph.Graph
Finds the community structure of the graph using the Leiden algorithm of Traag, van Eck & Waltman.
Parameters  edge_weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
node_weights  the node weights used in the Leiden algorithm.  
resolution_parameter  the resolution parameter to use. Higher resolutions lead to more smaller communities, while lower resolutions lead to fewer larger communities.  
normalize_resolution  if set to true, the resolution parameter will be divided by the sum of the node weights. If this is not supplied, it will default to the node degree, or weighted degree in case edge_weights are supplied.  
beta  parameter affecting the randomness in the Leiden algorithm. This affects only the refinement step of the algorithm.  
initial_membership  if provided, the Leiden algorithm will try to improve this provided membership. If no argument is provided, the aglorithm simply starts from the singleton partition.  
n_iterations  the number of iterations to iterate the Leiden algorithm. Each iteration may improve the partition further.  
Returns  the community membership vector. 
igraph.Graph
Finds the community structure of the graph according to the random walk method of Latapy & Pons.
The basic idea of the algorithm is that short random walks tend to stay in the same community. The method provides a dendrogram.
Parameters  weights  name of an edge attribute or a list containing edge weights 
steps  Undocumented  
Returns  a tuple with the list of merges and the modularity scores corresponding to each merge  
See Also  modularity()  
Unknown Field: attention  this function is wrapped in a more convenient syntax in the derived class Graph . It is advised to use that instead of this version.  
Unknown Field: newfield  ref  Reference 
Unknown Field: ref  Pascal Pons, Matthieu Latapy: Computing communities in large networks using random walks, http://arxiv.org/abs/physics/0512106. 
Internal function, undocumented.
Use igraph.Matching.is_maximal
instead.
Internal function, undocumented.
See Also  igraph.Graph.maximum_bipartite_matching 
Performs a random walk of a given length from a given node.
Parameters  start  the starting vertex of the walk 
steps  the number of steps that the random walk should take  
mode  whether to follow outbound edges only ("out" ), inbound edges only ("in" ) or both ("all" ). Ignored for undirected graphs.@param stuck: what to do when the random walk gets stuck. "return" returns a partial random walk; "error" throws an exception.  
stuck  Undocumented  
Returns  a random walk that starts from the given vertex and has at most the given length (shorter if the random walk got stuck) 
__graph_as_capsule()
Returns the igraph graph encapsulated by the Python object as a PyCapsule
.A PyCapsule is practically a regular C pointer, wrapped in a Python object. This function should not be used directly by igraph users, it is useful only in the case when the underlying igraph object must be passed to other C code through Python.
Returns the memory address of the igraph graph encapsulated by the Python object as an ordinary Python integer.
This function should not be used directly by igraph users, it is useful only if you want to access some unwrapped function in the C core of igraph using the ctypes module.