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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.
Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.
博纳奇的一系列措施并没有改变邻接矩阵。阿尔法集中性用它的解决方案替代了邻接矩阵。子图集中性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是，不管邻接矩阵最初的转变是什么，所有这些方法都有共同的限制行为。随着贝塔系数趋近于零，指数收敛到度中心性。随着贝塔系数接近其最大值，指数收敛到特征值的中心性。
===Game-theoretic centrality===
===Game-theoretic centrality===
Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).
Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).
从所有其他节点或到所有其他节点的距离在无向图中是不相关的，但是在有向图中可能产生完全不同的结果(例如:。一个网站可以从传出链接获得高度的亲密度中心性，而从传入链接获得的亲密度中心性低)。
从所有其他节点或到所有其他节点的距离在无向图中是不相关的，但是在有向图中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高度的亲密度中心性，而从传入链接获得的亲密度中心性低)。
In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:
In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:
在一个(不一定是连通的)图中，调和中心性反转了封闭中心性定义中的和和和互反运算:
在一个(不一定是连通的)图中，调和中心性反转了封闭中心性定义中的和互反运算:
More compactly the betweenness can be represented as:
More compactly the betweenness can be represented as:
更确切地说，两者之间的关系可以表示为: