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On the connection between the eigen-vectors of weighted graphs and their subgraphs
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M. I. Skvortsova
Published/Copyright:
October 1, 2004
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, . . . , n, λ be an eigen-value of the graph G of multiplicity t ≥ 1, and
let X(i) = (
, . . . , 
), i = 1, . . . , t, be linearly independent eigen-vectors corresponding to this eigen-value. We obtain formulas representing the components 
of the eigen-vectors X(i) in terms of some characteristics of special subgraphs of the graph G, i = 1, . . . , t, j = 1, . . . , n. An
illustrative example is given.
Published Online: 2004-10-01
Published in Print: 2004-10-01
Copyright 2004, Walter de Gruyter
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Articles in the same Issue
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- The asymptotic behaviour of the complexity of the interval search on the Boolean cube in the class of balanced trees
- Properties of systems of defining relations for automata
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