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A nonparametric view of network models and Newman–Girvan and other modularities

  1. Peter J. Bickela,1 and
  2. Aiyou Chenb
  1. aUniversity of California, Berkeley, CA 94720; and
  2. bAlcatel-Lucent Bell Labs, Murray Hill, NJ 07974
  1. Edited by Stephen E. Fienberg, Carnegie Mellon University, Pittsburgh, PA, and approved October 13, 2009 (received for review July 2, 2009)

Abstract

Prompted by the increasing interest in networks in many fields, we present an attempt at unifying points of view and analyses of these objects coming from the social sciences, statistics, probability and physics communities. We apply our approach to the Newman–Girvan modularity, widely used for “community” detection, among others. Our analysis is asymptotic but we show by simulation and application to real examples that the theory is a reasonable guide to practice.

Footnotes

  • 1To whom correspondence should be addressed. E-mail: bickel{at}stat.berkeley.edu
  • Author contributions: P.J.B. and A.C. performed research and analyzed data.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/cgi/content/full/0907096106/DCSupplemental.

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