---
title: Spectral Graph Theory
description: Spectral graph theory studies the properties of graphs in relation to the eigenvalues and eigenvectors of their associated matrices. Learners will understand how to analyze network structure, connectivity, and graph partitioning.
category: mathematics
subcategory: graph-theory
difficulty: beginner, intermediate, advanced
url: /subject/spectral-graph-theory
---

# Spectral Graph Theory

Spectral graph theory studies the properties of graphs in relation to the eigenvalues and eigenvectors of their associated matrices. Learners will understand how to analyze network structure, connectivity, and graph partitioning.

## Available Resources

1 Books • 2 Courses • 1 Websites

## Courses

### 1. Spectral and Algebraic Graph Theory

Learn spectral and algebraic graph theory with this course by Daniel A. Spielman. Explore connections between linear algebra and graph properties!

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.cs.yale.edu/homes/spielman/561/

**Tags:** spectral-graph-theory, graph-laplacian, eigenvalues, expander-graphs, linear-algebra, algorithms

### 2. Topics in Theoretical Computer Science: An Algorithmist's Toolkit (MIT 18.409)

**Author:** Jonathan Kelner

Geometric and spectral techniques used in modern algorithm design, starting with spectral graph theory: graph Laplacians, spectral partitioning, Cheeger's inequality, expanders and random walks. 25 lecture-note files and problem sets equip learners to apply eigenvalue methods to algorithmic problems.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://ocw.mit.edu/courses/18-409-topics-in-theoretical-computer-science-an-algorithmists-toolkit-fall-2009/

**Tags:** spectral-graph-theory, graph-laplacian, cheeger-inequality, expander-graphs, random-walks

## Books

### 1. Spectral Graph Theory

**Author:** Fan R. K. Chung

Fan Chung's CBMS lecture monograph on the eigenvalues of the normalized graph Laplacian, covering isoperimetric and Cheeger inequalities, expanders, random walks, diameter bounds and quasi-random graphs; prepares readers with linear algebra and graph theory background to read research literature.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0821803158?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, graph-theory

## Websites

### 1. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

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