Generating graphs that approach a prescribed modularity

  • Authors:
  • S. Trajanovski;F. A. Kuipers;J. MartíN-HernáNdez;P. Van Mieghem

  • Affiliations:
  • Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, The Netherlands;Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, The Netherlands;Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, The Netherlands;Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, The Netherlands

  • Venue:
  • Computer Communications
  • Year:
  • 2013

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Abstract

Modularity is a quantitative measure for characterizing the existence of a community structure in a network. A network's modularity depends on the chosen partitioning of the network into communities, which makes finding the specific partition that leads to the maximum modularity a hard problem. In this paper, we prove that deciding whether a graph with a given number of links, number of communities, and modularity exists is NP-complete and subsequently propose a heuristic algorithm for generating graphs with a given modularity. Our graph generator allows constructing graphs with a given number of links and different topological properties. The generator can be used in the broad field of modeling and analyzing clustered social or organizational networks.