The fifth chapter explores the application of spectral graph theory to network data analysis. The chapter begins with an introduction to fundamental graph theory concepts, including undirected and directed graphs, graph connectivity, and matrix representations such as the adjacency and Laplacian matrices. It then discusses the variational characterization of eigenvalues and their significance in understanding the structure of graphs. The chapter highlights the spectral properties of the Laplacian matrix, particularly its role in graph connectivity and partitioning. Key applications, such as spectral clustering for community detection and the analysis of random graph models like Erdős–Rényi random graphs and stochastic blockmodels, are presented. The chapter concludes with a detailed exploration of graph partitioning algorithms and their practical implementations using Python.