Correlation and Autocorrelation of Data on Complex Networks

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.