School of Biological Sciences, Royal Holloway, University of London, Egham TW20 0EX, UK.
J R Soc Interface. 2011 Jul 6;8(60):1031-40. doi: 10.1098/rsif.2010.0524. Epub 2010 Dec 1.
The structure of many biological, social and technological systems can usefully be described in terms of complex networks. Although often portrayed as fixed in time, such networks are inherently dynamic, as the edges that join nodes are cut and rewired, and nodes themselves update their states. Understanding the structure of these networks requires us to understand the dynamic processes that create, maintain and modify them. Here, we build upon existing models of coevolving networks to characterize how dynamic behaviour at the level of individual nodes generates stable aggregate behaviours. We focus particularly on the dynamics of groups of nodes formed endogenously by nodes that share similar properties (represented as node state) and demonstrate that, under certain conditions, network modularity based on state compares well with network modularity based on topology. We show that if nodes rewire their edges based on fixed node states, the network modularity reaches a stable equilibrium which we quantify analytically. Furthermore, if node state is not fixed, but can be adopted from neighbouring nodes, the distribution of group sizes reaches a dynamic equilibrium, which remains stable even as the composition and identity of the groups change. These results show that dynamic networks can maintain the stable community structure that has been observed in many social and biological systems.
许多生物、社会和技术系统的结构可以用复杂网络来进行有用的描述。尽管这些网络通常被描绘为时间固定的，但它们本质上是动态的，因为连接节点的边会被切断和重新连接，而节点本身也会更新其状态。理解这些网络的结构要求我们理解创建、维护和修改它们的动态过程。在这里，我们基于共同进化网络的现有模型，来描述单个节点的动态行为如何产生稳定的总体行为。我们特别关注由具有相似属性（表示为节点状态）的节点内生形成的节点组的动态，并且证明，在某些条件下，基于状态的网络模块性与基于拓扑的网络模块性相比表现良好。我们表明，如果节点根据固定的节点状态重新连接它们的边，网络模块性会达到一个稳定的平衡，我们可以对其进行分析量化。此外，如果节点状态不是固定的，而是可以从相邻节点中采用，那么群组大小的分布就会达到动态平衡，即使群组的组成和身份发生变化，这种平衡也能保持稳定。这些结果表明，动态网络可以维持在许多社会和生物系统中观察到的稳定社区结构。
