A characterization of modularity in graphs

Yilun Shang
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 17, 2011, Number 3, Pages 10–12
Full paper (PDF, 121 Kb)


Authors and affiliations

Yilun Shang
Institute for Cyber Security, University of Texas at San Antonio
San Antonio, Texas 78249, USA


We present alternative expressions for modularity in graphs. Modularity is used as a measure to characterize the community of networks, which is one of the most important features in real-world networks, especially social networks.


  • Modularity
  • Community structure

AMS Classification

  • 05C50


  1. Arenas, A, A. Fernández, S. Gómez. Analysis of the structure of complex networks at different resolution levels. New J. Phys., 10 (2008) 053039
  2. Danon, L., A. Díaz-Guilera, J. Duch, A. Arenas. Comparing community structure identification. J. Stat. Mech.: Theory Exp., 2005 P09008
  3. Fortunato, S. Community detection in graphs. Phys. Rep., 486 (2010) 75–174
  4. Kumpula, J. M., J. Saramäki, K. Kaski, J. Kertész. Limited resolution in complex network community detection with Potts model approach. Eur. Phys. J. B, 56 (2007) 41–45
  5. Mieghem, P. V., X. Ge, P. Schumm, S. Trajanovski, H. Wang. Spectral graph analysis of modularity and assortativity. Phys. Rev. E, 82 (2010) 056113
  6. Newman, M. E. J. Modularity and community structure in networks. Proc. Natl. Acad. Sci., 103(2006) 8577–8582
  7. Newman, M. E. J., M. Girvan. Finding and evaluating community structure in networks. Phys. Rev. E, 69 (2004) 026113
  8. Weisstein, E. W. CRC Concise Encyclopedia of Mathematics. CRC Press, 2003

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Cite this paper

Shang, Y. (2011). A characterization of modularity in graphs. Notes on Number Theory and Discrete Mathematics, 17(3), 10-12.

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