Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, spectral graph theory is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of 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. Two graphs are called isospectral or cospectral if the adjacency matrices of the graphs have equal multisets of eigenvalues.

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