Relative Clustering Coefficient

TL;DR

This paper introduces the relative clustering coefficient, a new network metric that improves network comparison and property analysis by ignoring edges with zero probability, offering a more nuanced understanding of network structure.

Contribution

The paper proposes a novel relative clustering coefficient that extends the global clustering coefficient by focusing on edges with non-zero probability, enhancing network analysis.

Findings

Relative clustering coefficient better distinguishes network properties.

The new metric improves network comparison accuracy.

Model examples demonstrate advantages over traditional clustering coefficient.

Abstract

In this paper, we relatively extend the definition of global clustering coefficient to another clustering, which we call it relative clustering coefficient. The idea of this definition is to ignore the edges in the network that the probability of having an edge is 0. Here, we also consider a model as an example that using relative clustering coefficient is better than global clustering coefficient for comparing networks and also checking the properties of the networks.