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Size of nodal domains of the eigenvectors of a G n , p graph
Author(s) -
Huang Han,
Rudelson Mark
Publication year - 2020
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20925
Subject(s) - eigenvalues and eigenvectors , nodal , adjacency matrix , mathematics , combinatorics , graph energy , graph , discrete mathematics , graph power , line graph , physics , medicine , quantum mechanics , anatomy
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.

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