Configuration model for correlation matrices preserving the node strength

TL;DR

This paper introduces a configuration model for correlation matrices that preserves node strength, enabling more accurate null models for network analysis of multivariate data.

Contribution

The paper presents a novel maximum entropy-based algorithm to generate reference correlation matrices that maintain node strength, improving analysis of network properties.

Findings

The model effectively preserves node strength in generated correlation matrices.

Application to clustering coefficients and community detection demonstrates its utility.

Provides a new null model for statistical significance testing in network analysis.

Abstract

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices, such as those derived from random matrix theory, that partially preserve properties of the original matrix. We propose a model to generate such reference correlation and covariance matrices for the given matrix. Correlation matrices are often analysed as networks, which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node. Given this background, the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes, akin to configuration models for conventional networks. Our algorithm is derived from the maximum entropy principle. We will apply the proposed algorithm to measurement of clustering coefficients and community detection, both of which require a null model to assess the statistical significance of the obtained results.