Self-Organization of Topology and Weight Dynamics on Networks from Merging and Regeneration

We propose a model of weighted networks in which the structural evolution is coupled with weight dynamics. Based on a simple merging and regeneration process, the model gives powel-law distributions of degree, strength and weight, as observed in many real networks. It should be emphasized that, in our model, the nontrivial degree-strength correlation can be reproduced and in agreement with empirical data. Moreover, the size-growing evolution model is also presented to meet the properties of real-world systems.     

复杂网络研究概述

近年来，真实网络中小世界效应和无标度特性的发现激起了物理学界对复杂网路的研究热潮．复杂网络区别于以前广泛研究的规则网络和随机网络最重要的统计特征是什么?物理学家研究复杂网络的终极问题是什么?物理过程以及相关的物理现象对拓扑结构是否敏感?物理学家进入这一研究领域的原因和意义何在?复杂网络研究领域将来可能会向着什么方向发展?文章围绕上述问题，从整体上概述了复杂网络的研究进展．     

Synchronization speed of identical oscillators on community networks

Synchronizability of complex oscillators networks has attracted much research interest in recent years. In contrast, in this paper we investigate numerically the synchronization speed, rather than the synchronizability or synchronization stability, of identical oscillators on complex networks with communities. A new weighted community network model is employed here, in which the community strength could be tunable by one parameter δ. The results showed that the synchronization speed of identical oscillators on community networks could reach a maximal value when δ is around 0.1. We argue that this is induced by the competition between the community partition and the scale-free property of the networks. Moreover, we have given the corresponding analysis through the second least eigenvalue λ2 of the Laplacian matrix of the network which supports the previous result that the synchronization speed is determined by the value of λ2.