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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Katz centrality ： ウィキペディア英語版 Katz centrality In Social Network Analysis (SNA) there are various measures of centrality which determine the relative importance of an actor (or node) within the network. Katz centrality was introduced by Leo Katz in 1953 and is used to measure the degree of influence of an actor in a social network.〔 Unlike typical centrality measures which consider only the shortest path (the geodesic) between a pair of actors, Katz centrality measures influence by taking into account the total number of walks between a pair of actors.〔 ==Measuring Katz centrality == Katz centrality computes the relative influence of a node within a network by measuring the number of the immediate neighbors (first degree nodes) and also all other nodes in the network that connect to the node under consideration through these immediate neighbors. Connections made with distant neighbors are, however, penalized by an attenuation factor $\backslash alpha$.〔 Each path or connection between a pair of nodes is assigned a weight determined by $\backslash alpha$ and the distance between nodes as $\backslash alpha^d$. For example, in the figure on the right, assuming that John’s centrality is being measured and that $\backslash alpha\; =\; 0.5$. The weight assigned to each link that connects John with his immediate neighbors Jane and Bob will be $(0.5)^1\; =\; 0.5$. Jose connects to John indirectly through Bob, the weight assigned to this connection (composed of two links) will be $(0.5)^2\; =\; 0.25$. Similarly, weight assigned to the connection between Agneta and John through Aziz and Jane will be $(0.5)^3\; =\; 0.125$ and weight assigned to the connection between Agneta and John through Diego, Jose and Bob will be $(0.5)^4\; =\; 0.0625$. 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「Katz centrality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.