Spectral properties of networks with community structure

Sanjeev Chauhan, Michelle Girvan, and Edward Ott
Phys. Rev. E 80, 056114 – Published 24 November 2009; Erratum Phys. Rev. E 85, 029906 (2012)

Abstract

In this paper, we discuss the eigenspectra of networks with community structure. It is shown that in many cases, the spectrum of eigenvalues of the adjacency matrix of a network with community structure gives a clear indication of the number of communities in the network. In particular, for a network with N nodes and Nc communities, there will typically be Nc eigenvalues that are significantly larger than the magnitudes of all the other (NNc) eigenvalues. We discuss this property as well as its use and limitations for determining Nc.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 17 May 2009

DOI:https://doi.org/10.1103/PhysRevE.80.056114

©2009 American Physical Society

Erratum

Erratum: Spectral properties of networks with community structure [Phys. Rev. E 80, 056114 (2009)]

Sanjeev Chauhan, Michelle Girvan, and Edward Ott
Phys. Rev. E 85, 029906 (2012)

Authors & Affiliations

Sanjeev Chauhan*, Michelle Girvan, and Edward Ott

  • Department of Physics, University of Maryland, College Park, Maryland 20742, USA

  • *sanjeevk@umd.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 80, Iss. 5 — November 2009

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×