Reconstructing directed networks for better synchronization

TL;DR

This paper introduces a centrality-based reconstructing (CBR) method using PageRank to improve synchronization in directed networks by strategically manipulating links, outperforming degree-based and random methods.

Contribution

The paper presents a novel CBR method that enhances network synchronization by effectively restructuring links based on PageRank centrality, achieving near-optimal network configurations.

Findings

CBR method outperforms degree-based and random methods in synchronization tasks.

Networks reconstructed with CBR show narrower incoming degree distributions.

CBR accelerates convergence to synchronization in Kuramoto model simulations.

Abstract

In this paper, we studied the strategies to enhance synchronization on directed networks by manipulating a fixed number of links. We proposed a centrality-based reconstructing (CBR) method, where the node centrality is measured by the well-known PageRank algorithm. Extensive numerical simulation on many modeled networks demonstrated that the CBR method is more effective in facilitating synchronization than the degree-based reconstructing method and random reconstructing method for adding or removing links. The reason is that CBR method can effectively narrow the incoming degree distribution and reinforce the hierarchical structure of the network. Furthermore, we apply the CBR method to links rewiring procedure where at each step one link is removed and one new link is added. The CBR method helps to decide which links should be removed or added. After several steps, the resulted networks are very close to the optimal structure from the evolutionary optimization algorithm. The numerical simulations on the Kuramoto model further demonstrate that our method has advantage in shortening the convergence time to synchronization on directed networks.