Persistent spectral graph

Spectral graph theory

With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shall concentrate mainly on the adjacency matrix of (undirected) graphs, and also discuss briefly the Laplacian. We shall show that spectral properies (the eigenvalues and eigenvectors) of these matrices pro...

Spectral graph theory

Spectral graph theory

Spectral graph theory is a fast developing field in modern discrete mathematics with important applications in computer science, chemistry and operational research. By merging combinatorial techniques with algebraic and analytical methods it creates new approaches to hard discrete problems and gives new insights in classical Linear Algebra. The proposed minisymposium will bring together leading...

On Spectral Graph Drawing

The spectral approach for graph visualization computes the layout of a graph using certain eigenvectors of related matrices. Some important advantages of this approach are an ability to compute optimal layouts (according to specific requirements) and a very rapid computation time. In this paper we explore spectral visualization techniques and study their properties. We present a novel view of t...

Mirex2007 - Graph Spectral Method

We present a graph spectral approach in which melodies are represented as graphs, based on the intervals between the notes they are composed of. These graphs are then indexed into a database using their laplacian spectra as a feature vector. This laplacian spectrum is a good representative of the original melody. Consequently, range searching around the query spectrum returns similar melodies.