Zhao Ming, Zhou Changsong, Lü Jinhu, Lai Choy Heng
Department of Physics, National University of Singapore, Singapore.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 2):016109. doi: 10.1103/PhysRevE.84.016109. Epub 2011 Jul 25.
In this paper the effects of inter-community links on the synchronization performance of community networks, especially on the competition between individual community and the whole network, are studied in detail. The study is organized from two aspects: the number or portion of inter-community links and the connection strategy of inter-community links between different communities. A critical point is found in the competition of global network and individual communities. Increasing the number of inter-community links will enhance the global synchronizability but degrade the synchronization performance of individual community before this point. After that the individual community will synchronize better and better as part of the whole network because the community structure is not so prominent. The critical point represents a balance region where the individual community is maximally independent while the information transmission remains effective between different communities. Among various connection strategies, connecting nodes belonging to different communities randomly rather than connecting nodes with larger degrees are the most efficient way to enhance global synchronization of the network. However, the dynamical modularity is the reverse case. A preferential connection scheme linking most of the hubs from the communities will allow rather efficient global synchronization while maintaining strong dynamical clustering of the communities. Interestingly, the observations are found to be relevant in a realistic network of cat cortex. The synchronization state is just at the critical point, which shows a reasonable combination of segregated function in individual communities and coordination among them. Our work sheds light on principles underlying the emergence of modular architectures in real network systems and provides guidance for the manipulation of synchronization in community networks.
本文详细研究了社区间链接对社区网络同步性能的影响，特别是对单个社区与整个网络之间竞争的影响。该研究从两个方面展开：社区间链接的数量或比例，以及不同社区之间社区间链接的连接策略。在全球网络与单个社区的竞争中发现了一个临界点。在该点之前，增加社区间链接的数量会提高全局同步性，但会降低单个社区的同步性能。在此之后，由于社区结构不再那么突出，单个社区作为整个网络的一部分将同步得越来越好。这个临界点代表了一个平衡区域，在这个区域中，单个社区具有最大的独立性，同时不同社区之间的信息传输仍然有效。在各种连接策略中，随机连接属于不同社区的节点而不是连接度较大的节点是增强网络全局同步的最有效方法。然而，动态模块化情况则相反。一种优先连接方案，将来自各个社区的大多数枢纽连接起来，在保持社区强大动态聚类的同时，将允许相当高效的全局同步。有趣的是，这些观察结果在猫皮层的实际网络中也具有相关性。同步状态恰好处于临界点，这表明在单个社区中隔离功能与它们之间的协调达到了合理的结合。我们的工作揭示了实际网络系统中模块化架构出现的潜在原理，并为社区网络中的同步控制提供了指导。
