Symmetry-based coarse-graining of evolved dynamical networks

TL;DR

This paper explores how evolved, degree-regular networks with specific spectral properties exhibit symmetric motifs and backbone structures that influence their subdiffusive dynamics, providing insights into their coarse-grained organization.

Contribution

It introduces a symmetry-based coarse-graining method for evolved networks with prescribed spectral properties, linking network structure to dynamical behavior.

Findings

Evolved networks show symmetric motifs and backbone structures.

Backbone structures influence the network's spectral properties.

Coarse-grained models clarify how structures produce subdiffusive dynamics.

Abstract

Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are evolved to exhibit subdiffusive dynamics. Under the additional constraint of degree-regularity, the evolved networks display an abundance of symmetric motifs arranged into loops and long linear segments. Exploiting results from algebraic graph theory on symmetric networks, we find the underlying backbone structures and how they contribute to the spectrum. The resulting coarse-grained networks provide an intuitive view of how the anomalous diffusive properties can be realized in the evolved structures.