Intensity and coherence of motifs in weighted complex networks

TL;DR

This paper introduces measures of intensity and coherence for motifs in weighted networks, generalizing traditional unweighted network metrics, and demonstrates their impact on analyzing financial and metabolic networks.

Contribution

It proposes new metrics for weighted networks, extending motif analysis and clustering coefficients to incorporate link weights.

Findings

Weighted measures can significantly alter network analysis conclusions.

Application to financial and metabolic networks shows the importance of weights.

Inclusion of weights provides deeper insights into local network structures.

Abstract

The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this approach. In this Letter we generalize this method for weighted networks. We introduce subgraph intensity as the geometric mean of its link weights and coherence as the ratio of the geometric to the corresponding arithmetic mean. Using these measures, motif scores and clustering coefficient can be generalized to weighted networks. To demonstrate these concepts, we apply them to financial and metabolic networks and find that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics.