Synchronization of degree correlated physical networks

TL;DR

This paper investigates how negative degree correlation in networks of nonlinear oscillators enhances synchronizability, using a novel clustering methodology and analytical estimates to confirm the positive effect of disassortativity.

Contribution

It introduces a new method to characterize degree correlation and demonstrates that disassortative networks improve synchronizability through combined numerical and analytical analysis.

Findings

Disassortative networks show better synchronizability.

Degree correlation affects network synchronization.

Analytical estimates confirm numerical results.

Abstract

We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to characterise degree correlation based on clustering the network vertices in p classes according to their degrees. Using this strategy we construct networks with an assigned power law distribution but changing degree correlation properties. We find that the network synchronizability improves when the network becomes dissassortative, i.e. when nodes with low degree are more likely to be connected to nodes with higher degree. Our numerical observations are confirmed by the analytical estimates found in this letter using an innovative approach based on the use of graph theoretical results.