Cliques and a new measure of clustering: with application to U.S. domestic airlines

TL;DR

This paper introduces a higher-order clustering measure extending the traditional clustering coefficient to larger node groups, providing insights into airline network structures.

Contribution

It presents a new higher-order clustering measure, with analytic formulas for small groups, and applies it to analyze U.S. airline network dynamics.

Findings

New higher-order clustering measure proposed

Analytic formulas for groups of 3, 4, and 5 nodes

Applied to U.S. airline networks to reveal structural changes

Abstract

We propose a higher-order generalization of the well-known overall clustering coefficient for triples $C(3)$ to any number of nodes. We give analytic formulae for the special cases of three, four, and five nodes and show that they have very fast runtime performance for small graphs. We discuss some theoretical properties and limitations of the new measure, and use it to provide insight into dynamic changes in the structure of U.S. airline networks.