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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 Conductance (graph) ： ウィキペディア英語版 Conductance (graph) In graph theory the conductance of a graph ''G''=(''V'',''E'') measures how "well-knit" the graph is: it controls how fast a random walk on ''G'' converges to a uniform distribution. The conductance of a graph is often called the Cheeger constant of a graph as the analog of its counterpart in spectral geometry. Since electrical networks are intimately related to random walks with a long history in the usage of the term "conductance", this alternative name helps avoid possible confusion. The conductance of a cut $(S,\; \backslash bar\; S)$ in a graph is defined as: :$\backslash varphi(S)\; =\; \backslash frac\}$ where the $a\_$ are the entries of the adjacency matrix for ''G'', so that :$a(S)\; =\; \backslash sum\_\; \backslash sum\_\; a\_$ is the total number (or weight) of the edges incident with ''S''. The conductance of the whole graph is the minimum conductance over all the possible cuts: : $\backslash phi(G)\; =\; \backslash min\_\backslash varphi(S).$ Equivalently, conductance of a graph is defined as follows: : $\backslash phi(G)\; :=\; \backslash min\_\backslash frac\}.\backslash ,$ For a ''d''-regular graph, the conductance is equal to the isoperimetric number divided by ''d''. ==Generalizations and applications== In practical applications, one often considers the conductance only over a cut. A common generalization of conductance is to handle the case of weights assigned to the edges: then the weights are added; if the weight is in the form of a resistance, then the reciprocal weights are added. The notion of conductance underpins the study of percolation in physics and other applied areas; thus, for example, the permeability of petroleum through porous rock can be modeled in terms of the conductance of a graph, with weights given by pore sizes. Conductance also helps measure the quality of a clustering. The maximum among the conductance of clusters provides a bound which can be used, along with inter-cluster edge weight, to define a measure on the quality of clustering. Intuitively, the conductance of a cluster(which can be seen as a set of vertices in a graph) should be low. Apart from this, the conductance of the subgraph induced by a cluster(called "internal conductance") can be used as well. 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「Conductance (graph)」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.