Entangled networks, synchronization, and optimal network topology

TL;DR

Entangled networks are a newly introduced class of graphs with highly homogeneous, interwoven structures that optimize synchronization, robustness, and communication efficiency, making them potentially valuable for various scientific fields.

Contribution

The paper introduces entangled networks, a novel class of graphs with optimal synchronization and flow properties, characterized by homogeneous and highly interconnected structures.

Findings

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

They exhibit short average distances and large loops with no clear community structure.

These networks outperform others in robustness, random walk efficiency, and communication tasks.

Abstract

A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node-distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community-structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost-optimal in many senses, and with plenty of potential applications computer science or neuroscience.