Eigenvectors of random graphs: Nodal Domains
نویسندگان
چکیده
منابع مشابه
Eigenvectors of Random Graphs: Nodal Domains
We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relatively little is known about the corresponding eigenvectors. Our main focus in this paper is on the nodal domains associated with the different eigenfunctions. In the analogous realm of Laplacians of Riemannian manifolds,...
متن کاملEigenvectors of Random Graphs : Delocalization and Nodal Domains
We study properties of the eigenvectors of adjacency matrices of G(n, p) random graphs, for p = ω(logn)/n. This connects to similar investigations for other random matrix models studied in physics and mathematics. Motivated by the recent paper of Dekel, Lee and Linial we study delocalization properties of eigenvectors and their connection to nodal domains. We show the following for an eigenvect...
متن کاملEntrywise Bounds for Eigenvectors of Random Graphs
Let G be a graph randomly selected from Gn,p, the space of Erdős-Rényi Random graphs with parameters n and p, where p > log 6 n n . Also, let A be the adjacency matrix of G, and v1 be the first eigenvector of A. We provide two short proofs of the following statement: For all i ∈ [n], for some constant c > 0
متن کاملSparse random graphs: Eigenvalues and eigenvectors
In this paper we prove the semi-circular law for the eigenvalues of regular random graph Gn,d in the case d→∞, complementing a previous result of McKay for fixed d. We also obtain a upper bound on the infinity norm of eigenvectors of Erdős-Rényi random graph G(n, p), answering a question raised by Dekel-Lee-Linial.
متن کاملIndependence Ratio and Random Eigenvectors in Transitive Graphs
1.1. The independence ratio and the minimum eigenvalue. An independent set is a set of vertices in a graph, no two of which are adjacent. The independence ratio of a graph G is the size of its largest independent set divided by the total number of vertices. If G is regular, then the independence ratio is at most 1/2, and it is equal to 1/2 if and only if G is bipartite. The adjacency matrix of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2010
ISSN: 1042-9832
DOI: 10.1002/rsa.20330