EigenvectorCentrality

EigenvectorCentrality[g]
给出图 g 中的顶点的特征向量中心度组成的列表.

EigenvectorCentrality[g,"In"]
给出一个有向图 g 的内中心度组成的列表.

EigenvectorCentrality[g,"Out"]
给出一个有向图 g 的外中心度组成的列表.

更多信息和选项更多信息和选项

  • 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.
  • 是图 g 中邻接矩阵 的最大特征值时,我们有:
  • EigenvectorCentrality[g]c=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].c
    EigenvectorCentrality[g,"In"]c=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].c 左特征向量
    EigenvectorCentrality[g,"Out"] 右特征向量
  • 特征向量中心度是经过规范化处理的.
  • 对于有向图 gEigenvectorCentrality[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.

背景
背景

  • 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.

范例范例打开所有单元关闭所有单元

基本范例  (2)基本范例  (2)

计算特征向量中心度:

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突出显示:

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对顶点排序. 与许多连接度很好的顶点相连接的顶点排在最前面.

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2010年引入
(8.0)
| 2012年更新
(9.0)