小世界网络与无标度网络的社区结构研究

模块性(modularity)是度量网络社区结构(community structure)的主要参数.探讨了Watts和Strogatz的小世界网络(简称W-S模型)以及Barabàsi 等的B-A无标度网络(简称B-A模型)两类典型复杂网络模块性特点.结果显示，网络模块性受到网络连接稀疏的影响，W-S模型具有显著的社区结构，而B-A模型的社区结构特征不明显.因此，应用中应该分别讨论网络的小世界现象和无标度特性.社区结构不同于小世界现象和无标度特性，并可以利用模块性区别网络类型，因此网络复杂性指标应该包括 关键词： 模块性 社区结构 小世界网络 无标度网络

Community structure in small-world and scale-free networks

Modularity is one on the important parameters to evaluate the community structure of network. The community structure of small-world networks (Watts-Strogatz model) and scale-free networks (Barabàsi-Albert model) were explored in the framework of the modularity using numerical simulations. We found that, firstly, the community structure in Watts' small-world networks is clear, while in Barabàsi's scale-free networks it is unclear; secondly, community structure is affected by the density of the network, namely, the sparser the network connections, the clearer is the community structure; thirdly, modularity in Watts' small-world networks is a dynamic variable which changes as a nonmonotonic function of the probability of rewiring connections. Hence, community structure should be one of the complex network properties. The real social networks may exhibit clear community structure, small-world phenomena and scale-free properties simultaneously. None of the current network models, such as the random network, Watts-Strogatz model, or Barabsi-Albert model, fits these social networks very well. A new social network structure is pending construction.