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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 Estrada index ： ウィキペディア英語版 Estrada index In chemical graph theory, the Estrada index is a topological index of protein folding. The index was first defined by Ernesto Estrada as a measure of the degree of folding of a protein, which is represented as a path-graph weighted by the dihedral or torsional angles of the protein backbone. This index of degree of folding has found multiple applications in the study of protein functions and protein-ligand interactions. The name of this index as the “Estrada index” was proposed by de la Peña et al. in 2007. ==Derivation== Let $G=(V,E)$ be a graph of size$|V|=n$ and let $\backslash lambda\; \_1\; \backslash geq\; \backslash lambda\; \_2\; \backslash geq\; ...\; \backslash geq\; \backslash lambda\; \_n$ be a non-increasing ordering of the eigenvalues of its adjacency matrix $A$ . The Estrada index is defined as $EE(G)=\backslash sum\_^n\; e^$ For a general graph, the index can be obtained as the sum of the subgraph centralities of all nodes in the graph. The subgraph centrality of node $i$ is defined as $EE(i)=\backslash sum\_^\; \backslash frac$ The subgraph centrality has the following closed form〔 $EE(i)=(e^A)\_=\backslash sum\_^()^2\; e^$ where $\backslash varphi\; \_j\; (i)$ is the $i$ th entry of the $j$th eigenvector associated with the eigenvalue $\backslash lambda\; \_j$ . It is straightforward to realise that〔 $EE(G)=tr(e^A)$ 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「Estrada index」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.