|
Betweenness centrality is an indicator of a node's centrality in a network. It is equal to the number of shortest paths from all vertices to all others that pass through that node. A node with high betweenness centrality has a large influence on the transfer of items through the network, under the assumption that item transfer follows the shortest paths. The concept finds wide application, including computer and social networks, biology, transport and scientific cooperation. Development of ''betweenness centrality'' is generally attributed to sociologist Linton Freeman. The idea was earlier proposed by mathematician J. Anthonisse, but his work was never published. == Definition == The betweenness centrality of a node is given by the expression: : is the total number of shortest paths from node to node and is the number of those paths that pass through . Note that the betweenness centrality of a node scales with the number of pairs of nodes as implied by the summation indices. Therefore the calculation may be rescaled by dividing through by the number of pairs of nodes not including , so that . The division is done by for directed graphs and for undirected graphs, where is the number of nodes in the giant component. Note that this scales for the highest possible value, where one node is crossed by every single shortest path. This is often not the case, and a normalization can be performed without a loss of precision : which results in: : : Note that this will always be a scaling from a smaller range into a larger range, so no precision is lost. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「betweenness centrality」の詳細全文を読む スポンサード リンク
|