Weighted network modules

TLDR

Including link weights in network analysis yields deeper insight into the often overlapping modular structure of real‑world webs. The study introduces a weighted clique percolation method (CPMw) that clusters weighted networks by percolating high‑intensity k‑cliques. CPMw permits overlapping modules, and the authors derive analytical and numerical results for the percolation threshold on weighted Erdős–Rényi graphs, then apply the method to a scientist collaboration web and a stock correlation graph to compute weight correlations and identify weighted modules. Reshuffling link weights and comparing to randomized controls shows that groups of three or more strong links preferentially cluster together in both the collaboration and stock networks.

Abstract

The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm clique percolation method with weights (CPMw) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdős–Rényi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomized control graphs as well, we show that groups of three or more strong links prefer to cluster together in both original graphs.