A new measure for community structures through indirect social connections

TL;DR

This paper introduces a novel weighted clustering coefficient based on a generalized triangle concept, enhancing community detection insights in social and biological networks.

Contribution

It proposes a new definition of triangles and clustering coefficient for weighted networks, extending traditional measures to better capture community structures.

Findings

Empirical validation on US airport networks shows improved community detection.

Application to C. elegans nervous system demonstrates the measure's usefulness.

Comparison indicates advantages over standard clustering coefficient definitions.

Abstract

Based on an expert systems approach, the issue of community detection can be conceptualized as a clustering model for networks. Building upon this further, community structure can be measured through a clustering coefficient, which is generated from the number of existing triangles around the nodes over the number of triangles that can be hypothetically constructed. This paper provides a new definition of the clustering coefficient for weighted networks under a generalized definition of triangles. Specifically, a novel concept of triangles is introduced, based on the assumption that, should the aggregate weight of two arcs be strong enough, a link between the uncommon nodes can be induced. Beyond the intuitive meaning of such generalized triangles in the social context, we also explore the usefulness of them for gaining insights into the topological structure of the underlying network. Empirical experiments on the standard networks of 500 commercial US airports and on the nervous system of the Caenorhabditis elegans support the theoretical framework and allow a comparison between our proposal and the standard definition of clustering coefficient.