网络的模块矩阵及其社团结构指标  

Modularity matrix of networks and the measure of community structure

作　　者：王高峡[1,2] 沈轶[2] 

机构地区：[1]三峡大学理学院,宜昌443002 [2]华中科技大学系统工程研究所,武汉430074

出　　处：《物理学报》2010年第2期842-850,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:60574025;60740430664);高等学校博士学科点专项科研基金(批准号:20070487052)资助的课题~~

摘　　要：探讨了复杂网络的模块矩阵的正(负)特征谱与网络的社团结构(反社团结构)的关系,给出了反映网络社团结构性质的相关定义.利用模块矩阵的多个特征值与特征向量,引入反映个体对所处社团的依附程度一种结构中心化指标.利用人工网络与实际网络数据,将这种指标与几种经典的中心化指标进行了比较.结果表明该指标具有较好的分辨率并与度指标具有一定程度的相关性.The relationships between positive （negative） eigenspectrums and the structure properties of community （anti-community） of complex networks are investigated, and some corresponding definitions are given. By using the multieigenspectrums of modularity matrix of networks, a kind of structural centrality measure called the community centrality, is introduced. This individual centrality measure describes the strength that the individual adheres to the corresponding community. The measure is illustrated and compared with the standard centrality measures using several artificial networks and real world networks data. The results show that the community centrality has better discrimination, and it has positive correlation with the degree centrality.

关 键 词：网络 模块矩阵 社团结构 中心化 

分 类 号：O157.5[理学—数学]