利用矩阵的特征向量求网络中的社团结构
Finding community structure in networks using the eigenvectors of matrices
摘要：
我们考虑在网络中检测社区或模块的问题，这些社区或模块是具有高于平均密度的连接它们的边的顶点组。以前的工作表明，一个强大的方法来解决这个问题是最大化的利益函数被称为“模块化”的网络可能的部门。在这里，我们表明，这个最大化的过程可以写在一个矩阵的特征谱，我们称之为模块化矩阵，它在社区检测中发挥的作用类似于图拉普拉斯在图分区计算中发挥的作用。这一结果导致我们的一些可能的算法检测社区结构，以及其他几个结果，包括一个频谱测量网络中的二分结构和一个新的中心性措施，确定这些顶点占据中心位置的社区内，他们属于。所提出的算法和措施，说明了各种现实世界的复杂网络的应用程序。
英文摘要：
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.
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