title: Multiple phases in modularity-based community detection.
abstract: Detecting communities in a network, based only on the adjacency matrix, is a problem of interest to several scientific disciplines. Recently, Zhang and Moore have introduced an algorithm [Proc. Natl. Acad. Sci. USA 111, 18144 (2014)], called mod-bp, that avoids overfitting the data by optimizing a weighted average of modularity (a popular goodness-of-fit measure in community detection) and entropy (i.e., number of configurations with a given modularity). The adjustment of the relative weight, the "temperature" of the model, is crucial for getting a correct result from mod-bp. In this work we study the many phase transitions that mod-bp may undergo by changing the two parameters of the algorithm: the temperature T and the maximum number of groups q. We introduce a new set of order parameters that allow us to determine the actual number of groups q̂, and we observe on both synthetic and real networks the existence of phases with any q̂∈{1,q}, which were unknown before. We discuss how to interpret the results of mod-bp and how to make the optimal choice for the problem of detecting significant communities.
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, 75205 Paris, France and Dipartimento di Fisica, Università di Roma "La Sapienza," Piazzale Aldo Moro 2, 00185 Rome, Italy.
authors.forename: Christophe
authors.initials: C
authors.lastname: Schülke
authors.affiliation: Dipartimento di Fisica, INFN-Sezione di Roma 1, and CNR-NANOTEC, UOS di Roma, Università di Roma "La Sapienza," Piazzale Aldo Moro 2, 00185 Rome, Italy.
authors.forename: Federico
authors.initials: F
authors.lastname: Ricci-Tersenghi