  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.

Social and Information Networks;Physics and Society