基于谱方法的复杂网络中社团结构的模块度

Modularity for community structure in complex networks based on spectral method

现实中的大量复杂网络表现出明显的社团结构,模块度是衡量网络社团结构划分的重要指标函数,但最常用的NG模块度存在分辨率限制问题,不能识别出小于一定规模的社团.文章在谱映射的基础上,提出了复杂网络社团结构的两种模块度.改进的表现模块度不仅能够应用于有权网络,而且部分解决了NG模块度的局限性问题;内聚模块度以社团内部的内聚度为衡量依据,从根本上避免了NG模块度和表现模块度可能出现的不恰当划分情况.最后通过计算机生成的测试网络和两个经典网络,与NG模块度对比验证了表现模块度和内聚模块度的可行性和有效性.

In reality many complex networks present community structures obviously. Modularity func- tion can evaluate the partitions of network community structure quantitatively. But the most popular NG＇s modularity may fail to identify communities smaller than a scale. In this paper, we proposed two modularities for community structure in complex network based on spectral method. The improvement performance modularity not only can apply in the weighted network, but also can overcome the resolution limit of NG＇s modularity partly. The cohesion modularity take the internal cohesion as the weight basis, and it essentially avoid the resolution limit of NG＇s modularity and performance modularity. Finally the proposed function has been tested on three networks, including the artificial networks and two classical real-world networks. Computational results demonstrate that the proposed modularities are feasible and effective by comparing with NG＇s modularity.