  We study the structure of loops in networks using the notion of modulus of
loop families. We introduce a new measure of network clustering by quantifying
the richness of families of (simple) loops. Modulus tries to minimize the
expected overlap among loops by spreading the expected link-usage optimally. We
propose weighting networks using these expected link-usages to improve
classical community detection algorithms. We show that the proposed method
enhances the performance of certain algorithms, such as spectral partitioning
and modularity maximization heuristics, on standard benchmarks.
