A mean-field analysis of community structure in social and kin networks

Details A mean-field analysis of community structure in social and kin networks A mean-field analysis of community structure in social and kin networks

2006-04-13

arxiv.org/abs/q-bio/0604016v1

Biology

Quantitative Biology

Populations and Evolution

31 pages, 4 figures

Scientific paper

We provide a mean-field analysis of community structure of social and biological networks assuming that actors are able to evaluate some tree-derived distance to the other actors and tend to aggregate with the less distant. We show that such networks have small components, and give exact descriptions for the probability distribution of a typical community size and the number of communities. In particular, we show that the probability distribution of the community size is well-approximated by a power-law distribution with exponent two. We illustrate the robustness of the mean-field analysis by comparing its predictions on previously studied social networks and biological data.

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