Spectral graph theory - Wikipedia
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 aim of this book is to understand the spectral grpah theory. We combine all classic sources, e.g. Fan Chung’s book, Dan Spielman and Luca Trevisan’s graduate courses.
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 …
There are three tasks that one must accomplish in the beginning of a course on Spectral Graph Theory: • One must convey how the coordinates of eigenvectors correspond to vertices in a …
Spectral graph theory is a vast and expanding area of combinatorics. We start these notes by introducing and motivating classical matrices associated with a graph, and then show how to …
Eigenvalues and the Laplacian of a graph. 1.1. Introduction. 1.2. The Laplacian and eigenvalues. 1.3. Basic facts about the spectrum of a graph. 1.4. Eigenvalues of weighted graphs. 1.5. …
Lectures #11: Spectral Graph Theory, I Tim Roughgarden & Gregory Valiant∗ May 7, 2024 Spectral graph theory is the powerful and beautiful theory that arises from the following …