Endowing networks with desired symmetries and modular behavior

TL;DR

This paper presents a method to design networks with specific symmetries and modular structures by leveraging eigenvector centrality, enabling precise control over network organization and function.

Contribution

It introduces a novel approach to reverse engineer networks with desired symmetries and modular behavior using eigenvector centrality insights.

Findings

Successfully generates networks with specified symmetries.

Ensures modular organization reflects the designed structure.

Applicable to blueprinting networks for parallel functions.

Abstract

Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of reverse engineering, and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.