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A local perspective on community structure in multilayer networks

Published online by Cambridge University Press:  12 January 2017

LUCAS G. S. JEUB ,
MICHAEL W. MAHONEY ,
PETER J. MUCHA  and
MASON A. PORTER
LUCAS G. S. JEUB
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OX2 6GG, UK Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, IN 47408, USA (e-mail: lucasjeub@gmail.com)
MICHAEL W. MAHONEY
Affiliation:
International Computer Science Institute, Berkeley, CA 94704, USA Department of Statistics, University of California at Berkeley, Berkeley, CA 94720, USA (e-mail: mahoneymw@gmail.com)
PETER J. MUCHA
Affiliation:
Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA (e-mail: mucha@unc.edu)
MASON A. PORTER
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OX2 6GG, UK CABDyN Complexity Centre, University of Oxford, Oxford, OX1 1HP, UK Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095, USA (e-mail: mason@math.ucla.edu)
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Abstract

The analysis of multilayer networks is among the most active areas of network science, and there are several methods to detect dense “communities” of nodes in multilayer networks. One way to define a community is as a set of nodes that trap a diffusion-like dynamical process (usually a random walk) for a long time. In this view, communities are sets of nodes that create bottlenecks to the spreading of a dynamical process on a network. We analyze the local behavior of different random walks on multiplex networks (which are multilayer networks in which different layers correspond to different types of edges) and show that they have very different bottlenecks, which correspond to rather different notions of what it means for a set of nodes to be a good community. This has direct implications for the behavior of community-detection methods that are based on these random walks.

Keywords

community structureclusteringmultilayer networksrandom walksnetwork community profilesspectral graph theorypersonalized PageRank
Type
Research Article
Information
Network Science , Volume 5 , Special Issue 2: Modeling, Analysis, and Mining of Multilayer Networks , June 2017 , pp. 144 - 163
Copyright
Copyright © Cambridge University Press 2017 

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