Expansion of the conditional probability function in a network with nearest-neighbour degree correlations

TL;DR

This paper develops an expansion of the conditional probability function to better characterize higher-order degree correlations in complex networks, enabling detection of non-linear correlations beyond traditional measures.

Contribution

It introduces a new mathematical expansion for the conditional probability to parameterize and analyze complex degree correlations in networks.

Findings

Provides a method to detect non-linear degree correlations

Enhances understanding of higher-order network properties

Offers a new tool for network analysis

Abstract

A useful property of a network that can be used to characterize many systems is the degree distribution. However, many complex networks exhibit higher--order degree correlations that must be studied through other means, such as clustering coefficients, the Newman r factor, and the average nearest neighbour degree (ANND). In this paper we develop an expansion of the conditional probability that can be used to parameterize such degree correlations. The measures of degree correlations associated with this expansion can be used to signal the presence of non--linear correlations.