Add to ORKGWe 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, nodal domains have been the subject of intensive research for well over a hundred years. Graphical nodal domains turn out to have interesting and unexpected properties. Our main theorem asserts that there is a constant c such that for almost every graph G, each eigenfunction of G has at most two large nodal domains, and in addition at most c exceptio...
In this thesis, we study high dimensional phenomena arising in convexity and probablistic combinator...
In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunct...
We start by reviewing the notion of "quantum graph", its eigenfunctions and the problem of counting ...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. He...
Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. He...
AbstractEigenvectors of the Laplacian of a graph G have received increasing attention in the recent ...
Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. He...
The Discrete Nodal Domain Theorem states that an eigenfunction of the k-th largest eigenvalue of a g...
Abstract. We describe extensive computational experiments on spectral proper-ties of random objects-...
The Discrete Nodal Domain Theorem states that an eigenfunction of the k-th largest eigenvalue of a g...
We describe extensive computational experiments on spectral properties of random objects— random cub...
In this thesis, we study high dimensional phenomena arising in convexity and probablistic combinator...
In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunct...
We start by reviewing the notion of "quantum graph", its eigenfunctions and the problem of counting ...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. He...
Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. He...
AbstractEigenvectors of the Laplacian of a graph G have received increasing attention in the recent ...
Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. He...
The Discrete Nodal Domain Theorem states that an eigenfunction of the k-th largest eigenvalue of a g...
Abstract. We describe extensive computational experiments on spectral proper-ties of random objects-...
The Discrete Nodal Domain Theorem states that an eigenfunction of the k-th largest eigenvalue of a g...
We describe extensive computational experiments on spectral properties of random objects— random cub...
In this thesis, we study high dimensional phenomena arising in convexity and probablistic combinator...
In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunct...
We start by reviewing the notion of "quantum graph", its eigenfunctions and the problem of counting ...