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Conference Papers Year : 2006

A Quality Measure for Multi-Level Community Structure


Mining relational data often boils down to computing clusters, that is finding sub-communities of data elements forming cohesive sub-units, while being well separated from one another. The clusters themselves are sometimes terms “communities” and the way clusters relate to one another is often referred to as a “community structure”. We study a modularity criterionMQ introduced by Mancoridis et al. in order to infer community structure on relational data. We prove a fundamental and useful property of the modularity measure MQ, showing that it can be approximated by a gaussian distribution, making it a prevalent choice over less focused optimization criterion for graph clustering. This makes it possible to compare two different clusterings of a same graph as well as asserting the overall quality of a given clustering relying on the fact that MQ is gaussian. Moreover, we introduce a generalization extending MQ to hierarchical clusterings of graphs which reduces to the original MQ when the hierarchy becomes flat.
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Dates and versions

lirmm-00091339 , version 1 (05-09-2006)


  • HAL Id : lirmm-00091339 , version 1


Maylis Delest, Jean-Marc Fédou, Guy Melançon. A Quality Measure for Multi-Level Community Structure. SYNASC'06: 8th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Sep 2006, pp.63-68. ⟨lirmm-00091339⟩
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