Weighted network modules

TL;DR

This paper introduces CPMw, a new clustering algorithm for weighted networks that identifies overlapping modules based on high-intensity k-cliques, providing insights into the modular structure of real-world networks.

Contribution

The paper presents CPMw, a novel weighted network clustering method based on percolating k-cliques, with analytical results and applications to real-world networks.

Findings

Strong links tend to cluster together in real-world networks.

Weighted modules reveal overlapping community structures.

The algorithm performs well on empirical network data.

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 (CPMw, Clique Percolation Method with weights) 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) Erdos-Renyi 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 randomised control graphs as well, we show that groups of 3 or more strong links prefer to cluster together in both original graphs.