Correlation and Autocorrelation of Data on Complex Networks

TL;DR

This paper explores how spatial data analysis techniques like Moran's autocorrelation can be adapted for complex networks with node-associated data, introducing null models and demonstrating their application on real and synthetic networks.

Contribution

It introduces methods for applying autocorrelation measures to non-spatial networks and proposes null models for significance testing.

Findings

Effective measures of global and local autocorrelation for network data

Null models for significance testing in network autocorrelation analysis

Demonstrated application on real and synthetic networks

Abstract

Networks where each node has one or more associated numerical values are common in applications. This work studies how summary statistics used for the analysis of spatial data can be applied to non-spatial networks for the purposes of exploratory data analysis. We focus primarily on Moran-type statistics and discuss measures of global autocorrelation, local autocorrelation and global correlation. We introduce null models based on fixing edges and permuting the data or fixing the data and permuting the edges. We demonstrate the use of these statistics on real and synthetic node-valued networks.