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On a relationship between the eigenvectors of weighted graphs and their subgraphs
M. I. Skvortsova, I. V. Stankevich
Abstract:
We consider the problem of finding connections between eigen-vectors and
subgraphs of a weighted undirected graph $G$.
Let $G$ have $n$ vertices labelled $1,\ldots,n$, $\lambda$ be an eigen-value of the graph $G$ of multiplicity $t\ge 1$, and let $X^{(i)}=(x_1^{(i)},\ldots,x_n^{(i)})$, $i=1,\ldots,t$, be linearly independent eigen-vectors corresponding to this eigen-value. We obtain formulas representing the components $x_j^{(i)}$ of the eigen-vectors $X^{(i)}$ in terms of some characteristics of special subgraphs of the graph $G$, $i=1,\ldots,t$,
$j=1,\ldots,n$. An illustrative example is given.
Received: 23.01.2003
Citation:
M. I. Skvortsova, I. V. Stankevich, “On a relationship between the eigenvectors of weighted graphs and their subgraphs”, Diskr. Mat., 16:4 (2004), 32–40; Discrete Math. Appl., 14:6 (2004), 569–577
Linking options:
https://www.mathnet.ru/eng/dm173https://doi.org/10.4213/dm173 https://www.mathnet.ru/eng/dm/v16/i4/p32
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Abstract page: | 419 | Full-text PDF : | 236 | References: | 52 | First page: | 2 |
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