论文标题
网络中心度度量的路径和流动
Paths and flows for centrality measures in networks
论文作者
论文摘要
我们考虑必须在最大的ARC-DISHING路径序列中通过一个网络$ n $的子集$ x $的路径数量，连接两个顶点$ y $和$ z $。我们表明，当$ x $是单身人士时，该数字等于$ n $中的最大流量价值从$ y $到$ z $的最大流量价值与$ n $设置获得的网络中的最大流量价值从$ y $到$ z $，而零是ARCS事件的能力到$ x $。从理论上讲，这一事实证明了网络文献中这两个概念的共同识别。我们还表明，当$ | x | \ geq 2时，相同的平等不能保持相同，因此，自然可以定义涉及路径和流的两个概念上不同的组中心度度量，都扩大了经典的流动中心性。
We consider the number of paths that must pass through a subset $X$ of vertices of a network $N$ in a maximum sequence of arc-disjoint paths connecting two vertices $y$ and $z$. We show that when $X$ is a singleton, that number equals the difference between the maximum flow value from $y$ to $z$ in $N$ and the maximum flow value from $y$ to $z$ in the network obtained by $N$ setting to zero the capacities of arcs incident to $X$. That fact theoretically justifies the common identification of those two concepts in network literature. We also show that the same equality does not hold when $|X|\geq 2.$ Consequently, two conceptually different group centrality measures involving paths and flows can naturally be defined, both extending the classic flow betweenness centrality.
