On a relationship between the eigenvectors of weighted graphs and their subgraphs
Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 32-40
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.
@article{DM_2004_16_4_a3,
author = {M. I. Skvortsova and I. V. Stankevich},
title = {On a relationship between the eigenvectors of weighted graphs and their subgraphs},
journal = {Diskretnaya Matematika},
pages = {32--40},
year = {2004},
volume = {16},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2004_16_4_a3/}
}
M. I. Skvortsova; I. V. Stankevich. On a relationship between the eigenvectors of weighted graphs and their subgraphs. Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 32-40. http://geodesic.mathdoc.fr/item/DM_2004_16_4_a3/