基于社团检测的复杂网络中心性方法

论证了社团检测函数模块密度的优化进程能转化为核矩阵的特征谱分.基于核矩阵最大特征值对应的特征向量,提出了一种新的中心性方法,称为模块密度中心性方法.与以往中心性度量方法不同,这种方法以模块密度检测复杂网络中的社团结构为基础,度量了第一个节点到它分配社团上的贡献,对社团的贡献越大,该节点的中心性值越高,反之亦然.通过合成网络和标准数据集网络,验证了该方法,并同其他中心性方法进行了比较,实验表明提出的模块密度中心性方法对网络中关键节点有更好的解和稳定性.进一步在计算机产生的两个大的随机网络和来自现实世界的两个大的复杂网络中,研究了模块密度中心性方法的统计分布.结果表明了提出的中心性方法能够刻画复杂网络的拓扑结构属性.

A centrality measure based on spectral optimization of modularity density

We show that the optimization process of modularity density can be written in terms of the eigen- spectrum of kernel matrix. Based on the eigenvectors belonging to the largest eigenvalue of kernel matrix, we present a new structure centrality measure, called modularity density centrality. Different from the previous centrality approach, the modularity density centrality characterizes the contribution of each node to its assigned community in networks. Nodes corresponding to large contributions to the community have high centrality, and conversely for small ones. The measure is illustrated and compared with the standard centrality measures by using respectively an artificial example network and a classic network data set. Experimental results show the structural centrality measure is better able to distinguish node in terms of their structural roles in the network and has better stability. The statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real world. Experimental results show the proposed approach can characterizes true topological structure of the complex networks.