Size of nodal domains of the eigenvectors of a Gn, p graph. Issue 2 (16th April 2020) - Huang, Han; Rudelson, Mark
Abstract : 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.