Centrality measures in networks
Centrality measures in networks
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DOI：
10.1007/s00355-023-01456-4
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发表时间：
2016-08
影响因子：
0.9
通讯作者：
Francis Bloch;M. Jackson;Pietro Tebaldi
中科院分区：
文献类型：
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作者：
Francis Bloch;M. Jackson;Pietro Tebaldi
我们表明，在网络分析中突出的中心性度量都是基于相加可分离和线性处理的统计数据，这些统计数据捕获了节点在网络中的位置。这使我们能够提供一种中心性度量的分类法，将它们提取到两个维度上的变化：(i)它们利用了关于节点位置的哪些信息，以及（ii）这些信息如何作为与相关节点距离的函数进行加权。通常使用的关于节点位置的三种信息——我们称之为“节点统计”——是从给定节点到其他节点的路径，从给定节点到其他节点的行走，以及包含给定节点的其他节点之间的测地线。使用节点位置的统计数据，我们还描述了树的类型，使得中心性度量都一致，并且我们还讨论了识别一些基于路径的中心性度量的属性。
We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node’s position in the network. This enables us to provide a taxonomy of centrality measures that distills them to varying on two dimensions: (i) which information they make use of about nodes’ positions, and (ii) how that information is weighted as a function of distance from the node in question. The three sorts of information about nodes’ positions that are usually used—which we refer to as “nodal statistics”—are the paths from a given node to other nodes, the walks from a given node to other nodes, and the geodesics between other nodes that include a given node. Using such statistics on nodes’ positions, we also characterize the types of trees such that centrality measures all agree, and we also discuss the properties that identify some path-based centrality measures.