Generic criticality of community structure in random graphs

@article{Lipowski2013GenericCO,
  title={Generic criticality of community structure in random graphs},
  author={Adam Lipowski and Dorota Lipowska},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={90 3},
  pages={
          032815
        }
}
  • A. LipowskiDorota Lipowska
  • Published 23 December 2013
  • Economics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We examine a community structure in random graphs of size n and link probability p/n determined with the Newman greedy optimization of modularity. Calculations show that for p<1 communities are nearly identical with clusters. For p=1 the average sizes of a community s(av) and of the giant community s(g) show a power-law increase s(av)∼n(α') and s(g)∼n(α). From numerical results we estimate α'≈0.26(1) and α≈0.50(1) and using the probability distribution of sizes of communities we suggest that… 

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