Size of nodal domains of the eigenvectors of a Gn, p graph. Issue 2 (16th April 2020)

• Record Type: Journal Article
• Authors: Huang, Han; Rudelson, Mark
• Is Part Of: Random structures & algorithms. Volume 57:Issue 2(2020)
• Page Start: 393
• Page End: 438
• Publication Date: 2020-04-16
• Subjects: Random matrices -- Erdos‐Renyi graph -- nodal domains; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20925
• Languages: English
• ISSNs: 1042-9832

Abstract

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.