Enhancing synchronization by directionality in complex networks

TL;DR

This paper introduces the residual edge-betweenness gradient (REBG) method to improve network synchronization by assigning link directions, effectively avoiding failures seen in previous methods and enhancing synchronizability especially in community-structured networks.

Contribution

The paper presents the REBG method, a novel approach for direction assignment that outperforms previous methods like RDG in enhancing network synchronizability and avoiding synchronization failures.

Findings

REBG prevents synchronization failure in networks.

REBG improves synchronizability in community-structured networks.

REBG outperforms RDG in various network configurations.

Abstract

We proposed a method called residual edge-betweenness gradient (REBG) to enhance synchronizability of networks by assignment of link direction while keeping network topology and link weight unchanged. Direction assignment has been shown to improve the synchronizability of undirected networks in general, but we find that in some cases incommunicable components emerge and networks fail to synchronize. We show that the REBG method can effectively avoid the synchronization failure ($R=\lambda_{2}^{r}/\lambda_{N}^{r}=0$) which occurs in the residual degree gradient (RDG) method proposed in Phys. Rev. Lett. 103, 228702 (2009). Further experiments show that REBG method enhance synchronizability in networks with community structure as compared with the RDG method.