Laplacian matrix

名詞

(graph theory) A square n⨯n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.

日本語の意味

無向グラフの各頂点を表すn個の行と列に対応し、対角成分には各頂点の次数（その頂点に接続する辺の数）が記録され、非対角成分には対応する頂点間に辺が存在する場合は−1、存在しない場合は0が記録される正方行列。

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To determine the number of connected components in a network, one can analyze the multiplicity of the zero eigenvalue of the Laplacian matrix.

ネットワークの連結成分の数を求めるには、対角成分に頂点の次数を、非対角成分に隣接する頂点なら−1、それ以外は0を持つグラフのラプラシアン行列の零固有値の重複度を解析すればよい。

詳細

意味（1）

(graph theory) A square n⨯n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.

Laplacian matrices （ plural ）