Community Detection via Facility Location

In this paper we apply theoretical and practical results from facility location theory to the problem of community detection in networks. The result is an algorithm that computes bounds on a minimization variant of local modularity. We also define the concept of an edge support and a new measure of the goodness of community structures with respect to this concept. We present preliminary results and note that our methods are massively parallelizable.

💡 Research Summary

The paper introduces a novel approach to community detection by casting the problem as an instance of the Uncapacitated Facility Location Problem (UFL). Traditional community detection methods rely heavily on modularity maximization, which suffers from resolution limits and can become trapped in local optima. To address these issues, the authors first define a “local modularity” objective that they aim to minimize. They then map each node in a graph to a potential facility and each possible assignment of a node to a community to a binary decision variable. The cost of opening a facility corresponds to a penalty for creating a new community, while the assignment cost reflects the dissimilarity between two nodes (e.g., inverse edge weight or inverse common‑neighbor count).

By relaxing the binary constraints to continuous variables in the interval