给出图 g 中的顶点的特征向量中心度组成的列表.
给出一个有向图 g 的内中心度组成的列表.
给出一个有向图 g 的外中心度组成的列表.
- EigenvectorCentrality 对于与许多其他连接度很好的顶点相连接的顶点，给出高中心度.
- EigenvectorCentrality 给出中心度 组成的列表，这些中心度可以表示为邻节点的中心度的加权和.
- 当 是图 g 中邻接矩阵 的最大特征值时，我们有：
EigenvectorCentrality[g] EigenvectorCentrality[g,"In"] ， 左特征向量 EigenvectorCentrality[g,"Out"] ， 右特征向量
- 对于有向图 g，EigenvectorCentrality[g] 等价于 EigenvectorCentrality[g,"In"].
- 选项 WorkingPrecision->p 可用于控制在内部计算中所用的精度.
- EigenvectorCentrality returns a list of non-negative numbers ("eigenvector centralities", also known as Gould indices) that are particular centrality measures of the vertices of a graph. The returned centralities are always normalized so that they sum to 1. Eigenvector centrality is a measure of the centrality of a node in a network, based on the weighted sum of centralities of its neighbors. It therefore identifies nodes in the network that are connected to many other well-connected nodes. This measure has found applications in social networks, transportation, biology, and social sciences.
- For a connected undirected graph, the vector of eigenvector centralities satisfies the eigenvector equation , where is the largest eigenvalue of the graph's adjacency matrix . In other words, for a connected undirected graph, the vector of eigenvector centralities is given by the (suitably normalized) eigenvector of corresponding to its largest eigenvalue. For a disconnected undirected graph, the vector of eigenvector centralities is given by a (suitably normalized) weighted sum of connected component eigenvector centralities.
- For a connected directed graph, the in-centrality vector satisfies the equation and the out-centrality satisfies . An additional or argument may be specified to obtain a list of in-centralities or out-centralities, respectively, for a directed graph.
- EigenvectorCentrality returns machine numbers by default but supports a WorkingPrecision argument to allow high-precision or exact (by specifying Infinity as the precision) values to be computed. EigenvectorCentrality is a normalized special case of KatzCentrality with and . A related centrality is PageRankCentrality. Eigenvectors, Eigenvalues, and Eigensystem can be used to compute eigenproperties of a given square matrix, and AdjacencyMatrix to obtain the adjacency matrix of a given graph.