Relationship Between Structural Characters and Synchronizability of   Scale-free Networks
  Using Memory Tabu Search(MTS) algorithm, we investigate the relationship between structural characters and synchronizability of scale-free networks by maximizing and minimizing the ratio $Q$ of the eigenvalues of the coupling matrix by edge-intercrossing procedures. The numerical results indicate that clustering coefficient $C$, maximal betweenness $B_{max}$ are two most important factors to scale-free network synchronizability, and assortative coefficient $r$ and average distance $D$ are the secondary ones. Moreover, the average degree $<k>$ affects the relationship between above structural characters and synchronizability of scale-free networks, and the minimal $Q$ decreases when $<k>$ increases. 
Jian-Guo Liu, Yan-Zhong Dang, Qiang Guo, and Zhong-Tuo Wang