# Tolerating the Community Detection Resolution Limit with Edge Weighting - Physics > Physics and Society

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Abstract: Communities of vertices within a giant network such as the World-Wide Web arelikely to be vastly smaller than the network itself. However, Fortunato andBarth\-{e}lemy have proved that modularity maximization algorithms forcommunity detection may fail to resolve communities with fewer than$\sqrt{L-2}$ edges, where $L$ is the number of edges in the entire network.This resolution limit leads modularity maximization algorithms to havenotoriously poor accuracy on many real networks. Fortunato and Barth\-{e}lemy-sargument can be extended to networks with weighted edges as well, and we derivethis corollary argument. We conclude that weighted modularity algorithms mayfail to resolve communities with fewer than $\sqrt{W \epsilon-2}$ total edgeweight, where $W$ is the total edge weight in the network and $\epsilon$ is themaximum weight of an inter-community edge. If $\epsilon$ is small, then smallcommunities can be resolved.Given a weighted or unweighted network, we describe how to derive new edgeweights in order to achieve a low $\epsilon$, we modify the CNM- communitydetection algorithm to maximize weighted modularity, and show that theresulting algorithm has greatly improved accuracy. In experiments with anemerging community standard benchmark, we find that our simple CNM variant iscompetitive with the most accurate community detection methods yet proposed.

Autor: Jonathan W. Berry, Bruce Hendrickson, Randall A. LaViolette, Cynthia A. Phillips

Fuente: https://arxiv.org/