Efficient Rewirings for Enhancing Synchronizability of Dynamical Networks

TL;DR

This paper introduces an algorithm that optimizes the synchronizability of complex networks through iterative edge rewirings, producing Ramanujan graphs efficiently across various sizes and topologies.

Contribution

The authors develop a scalable rewiring algorithm that enhances network synchronizability and can generate Ramanujan graphs of arbitrary size and degree.

Findings

The method effectively improves synchronizability in diverse networks.

Optimized networks are Ramanujan graphs.

The algorithm scales well with network size.

Abstract

In this paper, we present an algorithm for optimizing synchronizability of complex dynamical networks. Based on some network properties, rewirings, i.e. eliminating an edge and creating a new edge elsewhere, are performed iteratively avoiding always self-loops and multiple edges between the same nodes. We show that the method is able to enhance the synchronizability of networks of any size and topological properties in a small number of steps that scales with the network size.Although we take the eigenratio of the Laplacian as the target function for optimization, we will show that it is also possible to choose other appropriate target functions exhibiting almost the same performance. The optimized networks are Ramanujan graphs, and thus, this rewiring algorithm could be used to produce Ramanujan graphs of any size and average degree.