Laplacian matrices of general complex weighted directed graphs

Finding Cliques in Directed Weighted Graphs Using Complex Hermitian Adjacency Matrices

Multipartite Separability of Laplacian Matrices of Graphs

Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying graphs. We provide further results on the multipartite separability of Laplacian matrices of graphs. In particular, we identify complete bipartite graphs wh...

Cheeger Inequalities for General Edge-Weighted Directed Graphs

We consider Cheeger Inequalities for general edge-weighted directed graphs. Previously the directed case was considered by Chung for a probability transition matrix corresponding to a strongly connected graph with weights induced by a stationary distribution. An Eulerian property of these special weights reduces these instances to the undirected case, for which recent results on multi-way spect...

On weighted directed graphs

Article history: Received 6 January 2011 Accepted 16 June 2011 Available online 18 July 2011 Submitted by S. Kirkland AMS classification: 05C50 05C05 15A18

Laplacian Matrices of Graphs: A Survey

Let G be a graph on n vertices. Its Laplacian matrix is the n-by-n matrix L(G) = D(G) A(G), where A(G) is the familiar (0, 1) adjacency matrix, and D(G) is the diagonal matrix of vertex degrees. This is primarily an expository article surveying some of the many results known for Laplacian matrices. Its six sections are: Introduction, The Spectrum, The Algebraic Connectivity, Congruence and Equi...