Fast and accurate determination of modularity and its effect size

Abstract

We present a fast spectral algorithm for community detection in complex networks. Our method searches for the partition with the maximum value of the modularity via the interplay of several refinement steps that include both agglomeration and division. We validate the accuracy of the algorithm by applying it to several real-world benchmark networks. On all these, our algorithm performs as well or better than any other known polynomial scheme. This allows us to extensively study the modularity distribution in ensembles of Erdős-Rényi networks, producing theoretical predictions for means and variances inclusive of finite-size corrections. Our work provides a way to accurately estimate the effect size of modularity, providing a $z$-score measure of it and enabling a more informative comparison of networks with different numbers of nodes and links.

23 pages, 6 figures

References in corpus (13)

• Modularity and community structure in networks
• Uncovering the overlapping community structure of complex networks in nature and society
• Finding community structure in networks using the eigenvectors of matrices
• Cooperative Game Theory Approaches for Network Partitioning
• The structure and dynamics of multilayer networks
• Statistical Mechanics of Community Detection
• Community Structure in Jazz
• Characterizing the dynamical importance of network nodes and links
• Efficient and exact sampling of simple graphs with given arbitrary degree sequence
• The entropic origin of disassortativity in complex networks
• When are networks truly modular?
• Partitioning and modularity of graphs with arbitrary degree distribution
• Degree correlations in directed scale-free networks

Cited by in corpus (5)

• Synchronization in networks with multiple interaction layers
• Finding network communities using modularity density
• Multi-resolution community detection in massive networks
• Reduced network extremal ensemble learning (RenEEL) scheme for community detection in complex networks
• Resolution limit revisited: community detection using generalized modularity density