加权网络权重自相似评判函数及其社团结构检测

The evaluation function of weight similarity and its application in community detection in weighted networks

提出了权重自相似性加权网络社团结构评判函数,并基于该函数提出一种谱分析算法检测社团结构,结果表明算法能将加权网络划分为同一社团内边权值分布均匀,而社团间边权值分布随机的社团结构.通过建立具有社团结构的加权随机网络分析了该算法的准确性,与WEO和WGN算法相比,在评判权重自相似的阈值系数取较小时,该算法具有较高的准确性.对于一个具有n个节点和c个社团的加权网络,社团结构检测的复杂度为O(cn2/2).通过设置评判权重自相似的阈值系数,可检测出能反映节点联系稳定性的层化性社团结构.这与传统意义上只将加权网络划分为社团中边权值较大而社团间边权值较小的标准不同,从另一个角度更好地提取了加权网络的结构信息.

An evaluation function of weight similarity in weighted network is proposed,and a spectral algorithm for detecting community structure based on the function is presented. The results show that the algorithm can divide the weighted network into several groups within each of them the edges＇ weights distribute uniformly but at random between them. The algorithm is analyzed by constructing random weighted networks with known community structure. Compared with WEO and WGN,the algorithm has high accuracy when the threshold coefficient takes small values. For a network with n nodes and c communities,the computation complexity of the algorithm is O（cn2 /2）. By setting different threshold coefficients,a special hierarchical organization which describes the various steady connections between nodes in groups can be discovered by the algorithm. It is different from the conventional concept of community detection in weighted networks which divides the weighted network into several groups in which the edges＇ weights are relatively larger than those in-between them,such that it extracts the information about the structure of weighted networks from another perspective.