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 graph, such …

The spectrum of a graph has proven itself to be surprisingly informative about that graph's characteristics, such as the diameter of a graph and its connectivity.

Intuitively expanders are graphs that connect well. For a set of vertices within an expander graph, we can expect it to have a lot of neighbours and that is why people like expanders.

May 1, 2025 · Outline Spectral graph theory intertwines the field of graph theory with linear algebra by studying a graph’s connectivity and structure.

Sep 27, 2016 · This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. On the one hand, there is, of course, the linear algebra that …

Figure 1: Spectral embeddings of the cycle on 20 nodes (top two figures), and the 20 × 20 grid (bottom two figures). Each figure depicts the embedding, with the red lines connecting points that are …

Spectral graph theory has applications to the design and analysis of approximation algorithms for graph partitioning problems, to the study of random walks in graph, and to the construction of expander …

Spectral Graph Theory is a branch of graph theory that focuses on studying the properties of graphs by analyzing the eigenvalues and eigenvectors of matrices associated with the graph.

In this lecture, we give an overview of spectral graph theory, where in we use tools from Linear Algebra to study graphs. We demonstrate how we can “read off” combinatorial properties of graphs from their …

May 19, 2025 · Discover foundational principles of spectral graph theory and how eigenvalues and eigenvectors uncover structure in discrete mathematics.