Comment on "Dynamics and Directionality in Complex Networks"

TL;DR

This paper critiques the residual degree gradient (RDG) method's effectiveness in network synchronization and introduces a residual betweenness gradient (RBG) method as an alternative solution.

Contribution

It identifies limitations of the RDG method in certain cases and proposes the RBG method to improve network synchronization.

Findings

RDG can cause synchronization failure in some networks

RBG method addresses RDG limitations

Proposed RBG enhances network synchronizability

Abstract

Authors of Phys. Rev. Lett. 103, 228702 (2009) claim that "The residual degree gradient (RDG) method can enhance thesynchronizability of networks by simply changing the direction of the links". In this paper, we argue that in some case the RDG method will lead to the failure of synchronization ($R=\lambda^{r}_{2}/\lambda^{r}_{N}=0$). Additionally, we also propose a so-called residual betweenness gradient (RBG) method to solve this problem.