First-passage times to quantify and compare structural correlations and heterogeneity in complex systems

Abstract

Quantifying heterogeneity and correlations in complex systems consisting of a large number of interacting elements is key to understand their emergent properties. Here, the authors propose a method based on the statistics of interclass mean first passage times or random walks, and use it to quantify in a non-parametric way the level of heterogeneity and the presence of correlations in multiscale complex systems, where nodes are associated to a discrete number of classes.