This book offers an introduction to key topics in spectral graph theory. In spectral graph theory, various properties of graphs are studied using methods from linear algebra, particularly through the eigenvalues and eigenvectors of different matrices that describe the graph structure. Various aspects of graph theory find applications within the field of data science.

In this book, the necessary foundations of abstract graph theory and linear algebra are covered in parallel, making it suitable for students in their early semesters. The book has been tested multiple times in one-semester-long lectures and is therefore well-suited as a basis for a course and a collection of exercises for instructors.

Gives a concise introduction to spectral graph theory Introduces abstract graph theory Provides an overview of the required methods of linear algebra

Autorentext

Kiyan Naderi ist wissenschaftlicher Mitarbeiter an der Carl von Ossietzky Universität Oldenburg Konstantin Pankrashkin ist Professor für Analysis und ihre Anwendungen an der Carl von Ossietzky Universität Oldenburg

Inhalt

Chapter 1. Elementary Theory.- Chapter 2. Graph Properties and Min-Max Principle.- Chapter 3. Partitions and Eigenfunctions.- Chapter 4. Planarity and Colin de Verdiére Invariant.