重布线分层无标度网络：对同步性和拓扑结构的影响
Rewiring hierarchical scale-free networks: Influence on synchronizability and topology
摘要：
许多现实世界的复杂网络同时表现出无标度行为和层次组织的拓扑特征。在这方面，确定性无标度[A.- L. Barabási \etal，Physica A，299，3（2001）]和伪分形无标度[S. N.多罗戈夫采夫\etal，物理学Rev. E，65，6（2002）]网络构成同时包含上述属性的显著模型。控制这种网络形成的规则是完全确定的。然而，现实世界的网络可能既不是完全确定的，也不是完全分层的。因此，我们建议在这里完美的分层无标度网络与随机重新布线的边缘作为实际的网络系统的更好的代表。特别是，我们保留了各种确定性网络的无标度分布，但在重新布线的同时连续放松了层次结构。我们利用主稳定性函数的框架来研究耦合在这种重连网络上的动力系统的同步性。有趣的是，这揭示了重新布线的过程能够显著增强，以及恶化所产生的网络的同步性。我们调查的影响重新布线的边缘上的重新布线的网络的拓扑性质，反过来，它们的关系，各自的拓扑结构的同步性。最后，我们将确定性无标度网络和伪分形无标度网络的同步性与随机无标度网络（使用经典的Barabási-Albert增长和偏好连接模型生成）进行了比较，发现后者比确定性网络更能促进同步性。
英文摘要：
Many real-world complex networks simultaneously exhibit topological features of scale-free behaviour and hierarchical organization. In this regard, deterministic scale-free [A.-L. Barabási \etal, Physica A, 299, 3 (2001)] and pseudofractal scale-free [S. N. Dorogovtsev \etal, Phy. Rev. E, 65, 6 (2002)] networks constitute notable models which simultaneously incorporate the aforementioned properties. The rules governing the formation of such networks are completely deterministic. However, real-world networks are presumably neither completely deterministic, nor perfectly hierarchical. Therefore, we suggest here perfectly hierarchical scale-free networks with randomly rewired edges as better representatives of practical networked systems. In particular, we preserve the scale-free degree distribution of the various deterministic networks but successively relax the hierarchical structure while rewiring them. We utilize the framework of master stability function in investigating the synchronizability of dynamical systems coupled on such rewired networks. Interestingly, this reveals that the process of rewiring is capable of significantly enhancing, as well as, deteriorating the synchronizability of the resulting networks. We investigate the influence of rewiring edges on the topological properties of the rewired networks and, in turn, their relation to the synchronizability of the respective topologies. Finally, we compare the synchronizability of deterministic scale-free and pseudofractcal scale-free networks with that of random scale-free networks (generated using the classical Barabási-Albert model of growth and preferential attachment) and find that the latter ones promote synchronizability better than their deterministic counterparts.
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