Comment on "Dynamics and Directionality in Complex Networks"

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.