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Free keywords:
cs.SI, Physics, Physics and Society, physics.soc-ph
Abstract:
Cliques (or quasi-cliques) are frequently used to model communities: a set of
nodes where each pair is (equally) likely to be connected. However, when
observing real-world communities, we see that most communities have more
structure than that. In particular, the nodes can be ordered in such a way that
(almost) all edges in the community lie below a hyperbola. In this paper we
present three new models for communities that capture this phenomenon. Our
models explain the structure of the communities differently, but we also prove
that they are identical in their expressive power. Our models fit to real-world
data much better than traditional block models, and allow for more in-depth
understanding of the structure of the data.
