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特征路径长度,聚类系数,介数,节点效率简介
 
来源:xjh  编辑:xjh  2018-05-17

特征路径长度:在无向无权图中,节点 Ni与节点 Nj之间的特征路径长度 Dij定义为连接这两个节点的最短路径上的边数。

The characteristic path length of a network is the average minimum number of connections that link any two nodes of the network. It quantifies global efficiency (in terms of inverse path length) or the capability for parallel information propagation of a network.

聚类系数是用来刻画网络局部连接特征的参数,对于度为 Ki的节点 Ni,其聚类系数定义为与节点Ni相连的 Ki个节点之间实际存在的边数 Ei与这些节点之间总的可能边数之比。

the clustering coefficient of a node  is defined as the proportion of connections among its neighbors, divided by the number of connections that could possibly exist between them. (Watts and Strogatz, 1998). The clustering coefficient  of a node represents how close its neighbors tend to cluster together. It quantifies the extent of local cliquishness or local efficiency of information transfer of a network.

Accordingly, the average clustering coefficient of a network is considered as a direct measure of its segregation (i.e the degree to which a network is organized into local specialized regions).


介数用来刻画网络中各节点(或边)的重要性,通过一个节点(或边)的最短路径的数目称之为该节点或边的介数。介数较高的节点(或边)通常对保持整个网络通讯的有效性较为重要。

The betweenness centrality of a node is the number of shortest paths between any two nodes that run through the node. These nodal metrics can be used to identify network hubs.

节点效率Ik是指节点k与网络中其他节点之间距离倒数之和的平均值。The efficiency of a node is the mean of the inverse of the minimum path length between the node and all other nodes in the network.


网络效率E是指网络中所有节点对之间距离倒数之和的平均值。

Global efficiency: The global efficiency of a network is the average inverse shortest path length (Latora and Marchiori, 2001). A short path length indicates that, on average, each node can reach other nodes  with  a path composed of only a few edges  (Sporns, 2010).  Thus, the global efficiency is one of the most elementary indicators of network’s integration (i.e the degree to which a network can share information between distributed regions).  




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