On weakly optimal partitions in modular networks

Details On weakly optimal partitions in modular networks On weakly optimal partitions in modular networks

2010-08-20

arxiv.org/abs/1008.3443v1

Computer Science

Social and Information Networks

Scientific paper

Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph. Then, it also became an objective function used to find good partitions, with high success. Nevertheless, some works have shown a scaling limit and certain instabilities when finding communities with this criterion. Modularity has been studied proposing several formalisms, as hamiltonians in a Potts model or laplacians in spectral partitioning. In this paper we present a new probabilistic formalism to analyze modularity, and from it we derive an algorithm based on weakly optimal partitions. This algorithm obtains good quality partitions and also scales to large graphs.

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