Spectral Graph Theory is a branch of mathematics that studies the properties of graphs through the eigenvalues and eigenvectors of matrices associated with them, such as the adjacency matrix or the Laplacian matrix. By analyzing these spectral properties, researchers can gain insights into various characteristics of the graph, including connectivity, clustering, and the presence of certain structures. This field has applications in diverse areas, including network analysis, chemistry, and computer science. For example, it can help in understanding the stability of networks, predicting the behavior of molecules, or optimizing algorithms for data processing.