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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 CheiRank ： ウィキペディア英語版 CheiRank The CheiRank is an eigenvector with a maximal real eigenvalue of the Google matrix $G^$ * constructed for a directed network with the inverted directions of links. It is similar to the PageRank vector, which ranks the network nodes in average proportionally to a number of incoming links being the maximal eigenvector of the Google matrix $G$ with a given initial direction of links. Due to inversion of link directions the CheiRank ranks the network nodes in average proportionally to a number of outgoing links. Since each node belongs both to CheiRank and PageRank vectors the ranking of information flow on a directed network becomes two-dimensional. ==Definition== For a given directed network the Google matrix is constructed in the way described in the article Google matrix. The PageRank vector is the eigenvector with the maximal real eigenvalue $\backslash lambda=1$. It was introduced in and is discussed in the article PageRank. In a similar way the CheiRank is the eigenvector with the maximal real eigenvalue of the matrix $G^$ * built in the same way as $G$ but using inverted direction of links in the initially given adjacency matrix. Both matrices $G$ and $G^$ * belong to the class of Perron–Frobenius operators and according to the Perron–Frobenius theorem the CheiRank $P^$ *_i and PageRank $P\_i$ eigenvectors have nonnegative components which can be interpreted as probabilities.〔 〕 Thus all $N$ nodes $i$ of the network can be ordered in a decreasing probability order with ranks $K^$ *_i, K_i for CheiRank and PageRank $P^$ *_i, P_i respectively. In average the PageRank probability $P\_i$ is proportional to the number of ingoing links with $P\_i\; \backslash propto\; 1/^\backslash beta$. For the World Wide Web (WWW) network the exponent $\backslash beta\; =1/(\backslash nu-1)\; \backslash approx\; 0.9$ where $\backslash nu\; \backslash approx\; 2.1$ is the exponent for ingoing links distribution.〔〔 In a similar way the CheiRank probability is in average proportional to the number of outgoing links with $P^$ *_i \propto 1/^ with $\backslash beta^$ * =1/(\nu^ *-1) \approx 0.6 where $\backslash nu^$ * \approx 2.7 is the exponent for outgoing links distribution of the WWW.〔〔 The CheiRank was introduced for the procedure call network of Linux Kernel software in, the term itself was used in Zhirov. While the PageRank highlights very well known and popular nodes, the CheiRank highlights very communicative nodes. Top PageRank and CheiRank nodes have certain analogy to authorities and hubs appearing in the HITS algorithm but the HITS is query dependent while the rank probabilities $P\_i$ and $P^$ *_i classify all nodes of the network. Since each node belongs both to CheiRank and PageRank we obtain a two-dimensional ranking of network nodes. It should be noted that there had been early studies of PageRank in networks with inverted direction of links〔 〕 but the properties of two-dimensional ranking had not be analyzed in detail. 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「CheiRank」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.