Journal
PHYSICAL REVIEW E
Volume 94, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.94.052315
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Funding
- U.S. National Science Foundation [DMS-1107796, DMS-1407207]
- Simons Foundation [396239]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1407207] Funding Source: National Science Foundation
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We demonstrate an equivalence between two widely used methods of community detection in networks, the method of modularity maximization and the method of maximum likelihood applied to the degree-corrected stochastic block model. Specifically, we show an exact equivalence between maximization of the generalized modularity that includes a resolution parameter and the special case of the block model known as the planted partition model, in which all communities in a network are assumed to have statistically similar properties. Among other things, this equivalence provides a mathematically principled derivation of the modularity function, clarifies the conditions and assumptions of its use, and gives an explicit formula for the optimal value of the resolution parameter.
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