In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the …

The spectrum of a graph may be computed in the Wolfram Language using Eigenvalues[AdjacencyMatrix[g]]. Precomputed spectra for many named graphs can be …

The (ordinary) spectrum of a graph is the spectrum of its (0,1) adjacency matrix. (There are other concepts of spectrum, like the Laplace spectrum or the Seidel spectrum, that are the spectrum …

Here are some basic facts about the graph spectrum. Lemma 2.4. Let G be any undirected simple graph with n vertices. Then. i=1 i = 0. i=1 deg(i). n, then E[G] = ;. 1 degmax. Proof. We only …

Basic facts about the spectrum of a graph. 1.4. Eigenvalues of weighted graphs. 1.5. Eigenvalues and random walks. Chapter 2. Isoperimetric problems. 2.1. History. 2.2. The Cheeger constant …

characteristic properties or structures of graphs from its spectrum as well to use spectral techniques to aid in the design of useful algorithms. This report first presents a brief survey of …

A graph is a set of vertices V that are connected by a set of edges E with a function ψthat maps edges to unordered pairs of vertices. Figure 1: An undirected graph

3 The Laplacian and Graph Drawing29 4 Adjacency matrices, Eigenvalue Interlacing, and the Perron-Frobenius Theorem34 II The Zoo of Graphs43 5 Fundamental Graphs44 6 Comparing …

Formally, a graph is a pair G= (V;E), where V is the vertex set. EˆV V is the edge set. We say that x˘yif (x;y) 2E. We could also add edge weights, directions to the edges, and there are …

We begin with basic but necessary de nitions in graph theory that are important to both describe and prove results in spectral graph theory. Then, we move to topics in linear algebra that are …