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We study the structure of loops in networks using the notion of modulus ofloop families. We introduce a new measure of network clustering by quantifyingthe richness of families of (simple) loops. Modulus tries to minimize theexpected overlap among loops by spreading the expected link-usage optimally. Wepropose weighting networks using these expected link-usages to improveclassical community detection algorithms. We show that the proposed methodenhances the performance of certain algorithms, such as spectral partitioningand modularity maximization heuristics, on standard benchmarks.

Network clustering and community detection using modulus of families of loops