If you are observing faculty members in a teachers’ lounge, are you interested in who speaks with whom, or are you also interested in who initiated the conversation? Who initiated the conversation and who responded might be more interesting than just recording the pairs of teachers who engaged in conversations.

Remler and Van Ryzin (2010) define theory as a logical explanation that proposes a causal process or mechanism that produces an outcome of interest

So, let's say you are interested in the number of collaborative exchanges that occur between teachers from two different grade levels in a complete network of teachers within one elementary school. First, you count the number of times these types of exchanges occur in the observed network and then permute these relational data lots and lots of times. With each permutation, you calculate the number of times this type of tie (collaborative exchanges between teachers from two different grade levels) occurs and compare this result to the original observed network. After this process of permuting and comparing, you can see how often the results of these permutations are the same as the original observed results: The more often the results of the permutations are the same as your observed data, the more likely that the pattern of exchanges in the observed data was due to chance. If, however, the results from the observed data are so unlikely when compared to the results of the permutations, then you are to conclude that your results are not the byproduct of chance. Therefore, this result would be considered statistically significant.

In many cases, network analysts are studying a particular network or set of networks and have no interest in generalizing to a larger population of such networks (either because there isn't any such population or because they simply do not care about generalizing to it in any probabilistic way)

equilibrium” status of the network

The distinction between the two, however, is not clear cut.

Tie strength has been a core idea throughout the network field, with weak ties serving as important bridges between different groups and strong ties being influential in behavioral adoption. Generally, weak ties are important for the spread of instrumental resources (e.g., work-related advice), while strong ties are important for expressive resources (e.g., guidance on personal matters) (Lin, 2001a). Stated another way, weak ties are important for transmitting information but less so for transmitting behavioral influence (Valente, 2010). Granovetter's (1973) classic work has laid much of the foundation for much of the work that has focused on the tie strength.

Finally, while most analyses of ego networks use simple graphs—binary data that simply indicate whether an undirected tie is present between two actors—it is possible to incorporate directed relations into ego network analysis.

Egocentric network data generated in this manner, however, cannot be used to describe the overall embeddedness of the networks in some larger population.

Egos and Alters

A Visual Comparison of Structural, Automorphic, and Regular Equivalence. Consider this a graph of a hypothetical hierarchy of a school district's organizational chart, which consists of three levels linked by supervisory relation. Depending on your preferred definition of equivalence, different positions will be identified.

ou can also increase the value of n, but this is not advisable, as it seems odd for actors to be in the same clique if they are three steps from one another.

By charting this process, you are able to identify whether there is a “core” group of actors at the center of the network, while others are on the periphery.

There is, however, no current standard for an acceptable Q value.

it is more sensible to report what is referred to as effective density, which is the number of lines (ties) multiplied by the number of possible alters:where L again is the number of lines (directed ties) in the network, N is network size, and λ is the maximum number of alters requested or permitted. Using this formula, the density of the Fraternity Data is 1.0: All possible relations are present, which is unsurprising given that the original ranked data were recoded (1–3 = 1, all others = 0) and each respondent had the maximum number of three friendship nominations.

network's boundaries

This approach is either based on your knowledge about relations among a set of actors or relies on the actors themselves to nominate additional actors for inclusion.

He reaches a higher volume of information because he reaches more students indirectly.

For example, Coleman claims that social capital is any “social-structural resource” that generates returns for someone in a specific action. Accordingly, social capital can be captured only by its effect; whether it is an investment depends on the [Page 221]return to a specific individual in a specific action (Lin, 2001b). Obviously, it is impossible to theorize social capital when its causes and effects are folded into a single function.

he concept of social capital is said to address all of these situations (Kadushin, 2004).

You are at home doing your homework and have no idea how to solve a math problem. But you can call a classmate and ask that they help you work through the answer. It was worth being nice to that classmate even though you do not particularly like him. Do you have to return the favor? Maybe he can grab a ride with you the next time your sibling gives you a ride home from school. Maybe the value of his help was minor enough that you feel little need to reciprocate. Now, however, you need help preparing for a big math exam. Your classmate has made a digital copy of the notes that the teacher prepared for the whole class that you left in your locker. But there is really nothing to return except for the goodwill, because although he passes on this digital copy, your classmate still has it. Another classmate that you have never spoken with has heard from this first classmate that you are real good at writing computer code and asks you to help him. You are busy but feel obligated to at least try and help because you are all in the same math class. Someday you may even have to ask that classmate, maybe even a different one, for help in fixing that computer. What goes around comes around. In fact, you may be in a bad mood because you got that homework question wrong, failed the math exam, and your computer is busted. Someone with whom you have been friends for years and do not see often calls you and makes you feel much better.[Page 216]

Two-Mode (Affiliation) Matrices

If schools are the actors, they too have multiple relations with other schools, including information exchange, alliances, partnerships, and other connections.

As noted by Hanneman and Riddle (2011a), a well-constructed graph can be very useful, perhaps even more useful than words, for communicating a network's properties.

A second area in which educational research has generated theoretical insights through social network analysis is the area of diffusion, particularly how innovations spread through and across organizations such as schools

Unfortunately, this divide still polarizes the field of educational research

dynamic process that is not adequately explained by conventional social theory, nor do the methods most often used by social scientists capture [Page 36]these dynamics

CONCOR (for CONvergence of iterated CORrelations)

therapeutic techniques

flow of social influence

whether through influence processes (e.g., individuals adopting their friends' occupational choices) or leveraging processes (e.g., an individual can get certain things done because of the connections she has to powerful others).