Clustering Coefficient of the Tensor Product of Graphs

TL;DR

This paper derives formulas and bounds for the clustering coefficient in tensor product graphs, enhancing understanding of this metric in complex network analysis.

Contribution

It provides new expressions and bounds for the clustering coefficient specifically in tensor product graphs, a less-explored area in graph theory.

Findings

Formulas for clustering coefficient of tensor product of arbitrary, regular, and strongly regular graphs.

A Vizing-type upper bound for the clustering coefficient.

A sharp lower bound for the clustering coefficient.

Abstract

Clustering coefficient is one of the most useful indices in complex networks. However, graph theoretic properties of this metric have not been discussed much in the literature, especially in graphs resulting from some binary operations. In this paper we present some expressions for the clustering coefficient of the tensor product of arbitrary graphs, regular graphs, and strongly regular graphs. A Vizing-type upperbound and a sharp lower bound for the clustering coefficient of the tensor product of graphs are also given.