In mathematics, spectral graph theory is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated to the graph, such as its adjacency matrix or Laplacian matrix.An undirected graph has a symmetric adjacency matrix and therefore has real eigenvalues (the multiset of which is called the graph's spectrum) and a complete set of orthonormal eigenvectors.While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant.Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdière number.