Size of nodal domains of the eigenvectors of a graph

Size of nodal domains of the eigenvectors of a graph

Consider an eigenvector of the adjacency matrix of a G ( n , p ) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonle...

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Veröffentlicht in:Random structures & algorithms 2020-09, Vol.57 (2), p.393-438
Hauptverfasser: Huang, Han, Rudelson, Mark
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Rudelson, Mark
description Consider an eigenvector of the adjacency matrix of a G ( n , p ) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other.
doi_str_mv 10.1002/rsa.20925
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title Size of nodal domains of the eigenvectors of a graph
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