复杂网络中社团结构发现的多分辨率密度模块度

摘要

现实中的许多复杂网络呈现出明显的模块性或社团性.模块度是衡量社团结构划分优劣的效益函数,它也通常被用作社团结构探测的目标函数,但最为广泛使用的Newman-Girvan模块度却存在着分辨率限制问题,多分辨率模块度也不能克服误合并社团和误分裂社团同时存在的缺陷.本文在网络密度的基础上提出了多分辨率的密度模块度函数,通过实验和分析证实了该函数能够使社团结构的误划分率显著降低,而且能够体现出网络社团结构是一个有机整体,不是各个社团的简单相加.%In reality many complex networks present modules or community structures obviously.Modularity is a benefit function used in quantifying the quality of a division of a network into communities.And it usually can be used as a basis for optimization methods of detecting community structure in networks.But the most popular modularity which is proposed by M.E.J.Newman and M.Girvan has the resolution limit in community detection.Multi-resolution modularity cannot overcome the misclassifications caused by merging and splitting the communities either.In this paper,we propose a multi-resolution density modularity based on the network density. The proposed function is tested on the artificial networks.Computational results show that it can reduce the rate of misclassification considerably.And the systematicness of the community structures can be demonstrated by the multi-resolution density modularity.