Synchronization in Network Structures: Entangled Topology as Optimal Architecture for Network Design

TL;DR

This paper explores the design of entangled network topologies that optimize synchronizability and robustness, demonstrating their superior performance in various network functions through simulated annealing.

Contribution

It introduces entangled networks as a novel topology optimized for synchronization, constructed via simulated annealing, with superior properties over traditional network structures.

Findings

Entangled networks have homogeneous degree, distance, and betweenness distributions.

They exhibit short average distances and high robustness.

They perform nearly optimally in flow, searchability, and first-passage times.

Abstract

In these notes we study synchronizability of dynamical processes defined on complex networks as well as its interplay with network topology. Building from a recent work by Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)], we use a simulated annealing algorithm to construct optimally-synchronizable networks. The resulting structures, known as entangled networks, are characterized by an extremely homogeneous and interwoven topology: degree, distance, and betweenness distributions are all very narrow, with short average distances, large loops, and small modularity. Entangled networks exhibit an excellent (almost optimal) performance with respect to other flow or connectivity properties such as robustness, random walk minimal first-passage times, and good searchability. All this converts entangled networks in a powerful concept with optimal properties in many respects.