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Asymptotic Modularity of Some Graph Classes

  • Fabien de Montgolfier
  • Mauricio Soto
  • Laurent Viennot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

Modularity has been introduced as a quality measure for graph partitioning. It has received considerable attention in several disciplines, especially complex systems. In order to better understand this measure from a graph theoretical point of view, we study the modularity of a variety of graph classes. We first consider simple graph classes such as tori and hypercubes. We show that these regular graph families have asymptotic modularity 1 (that is the maximum possible). We extend this result to the general class of unit ball graphs of bounded growth metrics. Our most striking result concerns trees with bounded degree which also appear to have asymptotic modularity 1. This last result can be extended to graphs with constant average degree and to some power-law graphs.

Keywords

Connected Graph Maximum Degree Average Degree Graph Partitioning Graph Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Fabien de Montgolfier
    • 1
  • Mauricio Soto
    • 1
  • Laurent Viennot
    • 2
  1. 1.LIAFAUMR 7089 CNRS - Université Paris DiderotFrance
  2. 2.INRIA and Université Paris DiderotFrance

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