title: Equivalence between modularity optimization and maximum likelihood methods for community detection.
abstract: 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.
authors.affiliation: Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: M E J
authors.initials: ME
authors.lastname: Newman