Generalizations of the clustering coefficient to weighted complex networks

TL;DR

This paper reviews and compares different methods for generalizing the clustering coefficient to weighted networks, highlighting their advantages and limitations through examples and empirical data.

Contribution

It provides a comprehensive comparison of existing weighted clustering coefficient measures and discusses their applicability to real-world networks.

Findings

Different generalizations have specific advantages and limitations.

Empirical data illustrates the practical differences between measures.

The study guides the choice of clustering coefficient measures for weighted networks.

Abstract

The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the clustering coefficient, which is one of the central characteristics in the complex network theory. We present a comparative study of the several suggestions introduced in the literature, and point out their advantages and limitations. The concepts are illustrated by simple examples as well as by empirical data of the world trade and weighted coauthorship networks.