网络同步：最优无标度拓扑和Pessimal无标度拓扑
Network synchronization: Optimal and Pessimal Scale-Free Topologies
摘要：
通过采用最近推出的优化算法，我们显式设计最佳同步（未加权）网络的任何给定的无标度分布。我们探讨了优化过程如何影响度的相关性，并观察到一个通用的倾向disprobability。尽管如此，我们表明，有没有一个一对一的对应关系之间的同步性和disprobability。另一方面，我们研究了最优非同步网络的性质，即网络的拓扑结构使同步状态的稳定范围最小化。由此产生的“悲观网络”结果是具有高度重复性的弦状结构。我们还推导出一个严格的拉普拉斯特征值比控制的同步性，这有助于理解度相关性对网络同步性的影响的下限。
英文摘要：
By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.
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