Robustness of community structure in networks

Brian Karrer, Elizaveta Levina, and M. E. J. Newman
Phys. Rev. E 77, 046119 – Published 29 April 2008

Abstract

The discovery of community structure is a common challenge in the analysis of network data. Many methods have been proposed for finding community structure, but few have been proposed for determining whether the structure found is statistically significant or whether, conversely, it could have arisen purely as a result of chance. In this paper we show that the significance of community structure can be effectively quantified by measuring its robustness to small perturbations in network structure. We propose a suitable method for perturbing networks and a measure of the resulting change in community structure and use them to assess the significance of community structure in a variety of networks, both real and computer generated.

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  • Received 24 September 2007

DOI:https://doi.org/10.1103/PhysRevE.77.046119

©2008 American Physical Society

Authors & Affiliations

Brian Karrer1, Elizaveta Levina2, and M. E. J. Newman1,3

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 2Department of Statistics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 3Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA

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Issue

Vol. 77, Iss. 4 — April 2008

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