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 } }
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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