Hierarchies appear where there is a clear gradient or flow. The canonical examples are river networks and trees (from which: dendritic).

Even here, flows are often not entirely directed -- a river system experiences evaporation, precipitation, ground seepage, and aquifer flows, in addition to its dominant gravity-induced current. A tree has flows which originate at leaves (photosynthesis) and roots (water, mineral sourcing), as well as elsewhere (flowers, parasites and symbiotes, community flora and fauna). Similarly, evolutionary trees represent not only ancestral inheritance, but cross-species gene transfers -- bacteria, viruses, mitochondria, even other higher-order organisms (generally through an intermediary).

A true ontology to me is a largely nondirected graph. This may be a union of several directed graphs, a region of low-directedness within a larger directed space, or (fairly rarely) a near-universal truly nondirected system. Given that even cosmological megastructures are defined in terms of attractors and repellers, that is: gradients, truly nondirected spaces seem. likely rare. Though that's describing physical entities, conceptual spaces seem to me similar -- at least analogous, perhaps even more than that.

A tremendous risk in conceptual spaces is to equate some gradient with a moral, ethical, or social value gradient. This isn't -always_ a mistake, but it very frequently at least obscures more than it reveals, and can cause tremendous harm. The trait and tendency seems quite innate, dating. to earliest histories and likely earlier in the sociological and anthropological. It's all but certainly part of our neural wiring, "human nature", if not far deeper than that: a fundamental trait of representational modelling systems operating under constraints of perceptions, models, prior data, and processing and response capacity. Hierarchical value judgements are, by fundamental constraints of information systems theory, necessary (and very flawed) heuristics.

Or in fewer words: all models are wrong, some are useful.

Because both personal and sociocultural identities become wedded with values, they become rigid and defining. Good if certainty, speed, and consistency are required, not so much when flexibility and adaptation are.

In the context of TFA (and yes I'd submitted this): both hierarchical and ontological constructs are useful. I most often tend to think along the multi-hierarchical model -- that there are numerous centres, attractors, and repellers, with some phenomena behaving as both: a star or galaxy radiates light whilst attracting matter -- the same phenomenon is both a source and a sink.

I see networks of elements, trends, or traits, often with gradients not only of intensity but of complexity. This ... seems to serve fairly well.

Also worth noting: it's fascinating looking at classification schemes throughout history and which of those had central organising principles now seen as utterly unfounded. As well as some which have survived, or at least strongly suggested modern schemas.

For informational classifications associated with physical records such as the Dewey Decimal or Library of Congress Classification, a key contraint is that records must exist within physical space, at one and only one location. Looking at other classification systems (say, the LoC Subject Headings), this constraint does not exist, and works can be described, non-hierarchically, under multiple subjects simultaneeously. At the same time, many of the subject sections themselves have a strongly hierarchical structure, though also with notable idiosyncracies within specific areas. The law classifications, to my mind, most especially so.