It's not that tree structures don't have to be hierarchical, it's that what you're describing is not a tree structure.This..."If we visualized all links in Luhmann's ZK, we would have a forest with many links between branches and trees."...is not a tree structure.Tree structures are by design hierarchical. They are meant to show "hereditary" (so to speak) relationships in a linear trajectory. This is accepted in more or less every discipline where they are employed. To equate Luhmann's ZK as having anything to do with that is just false. It's a mistake, and is, unfortunately, one that is regularly perpetuated.Even Schmidt (and by proxy Kieserling), who visually depict Luhmann's "analog" "branches" very much as a tree structure (aka a hierarchy) go out of their way to state on the Archive's website that having done so was an editorial decision done out of convenience and should not be taken literally or be read as representative of the structure of Luhmann's zettelkasten:"The hierarchization of the organizational structure carried out by the Niklas Luhmann archive is an editorial decision, the order of [Luhmann's zettelkasten] does not follow a strict hierarchy logic." (Schmidt)But, what about trees....?"A tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form." (guru wikipedia)For those in the back...."The zettelkasten is in no way a hierarchy." (Kieserling)And, in case there's any doubt (as many think the alphanumeric numbering schema is itself representative of a hierarchy), Schmidt couldn't be more clear:"[T]he number structure does not represent a hierarchical structure."What you're describing (see above) is more along the lines of a rhizome:"We will enter, then, by any point whatsoever; none matters more than another.... We will be trying only to discover what other points our entrance connects to, what crossroads and galleries one passes through to link two points, what is the map of the rhizome and how the map is modified if one enters by another point." (Deleuze and Guattari 1986: 3)Rhizomes are the antithesis of tree structures.“We’re tired of trees.... They’ve made us suffer too much.” (.ibid)

A filing system is indefinitely expandable, rhizomatic (at any point of timeor space, one can always insert a new card); in contradistinction with the sequen-tial irreversibility of the pages of the notebook and of the book, its interiormobility allows for permanent reordering (for, even if there is no narrative conclu-sion of a diary, there is a last page of the notebook on which it is written: its pagesare numbered, like days on a calendar).