The Graph Laplacian is a matrix representation of a graph that captures its structure and connectivity. It is defined using the degree matrix, which contains the degree of each vertex, and the adjacency matrix, which indicates connections between vertices. The Graph Laplacian is useful in various applications, including spectral clustering and image segmentation. In mathematical terms, the Graph Laplacian L is calculated as L = D - A , where D is the degree matrix and A is the adjacency matrix. This matrix helps analyze properties of the graph, such as its number of connected components and the behavior of random walks on the graph.