Spectral Graph Theory
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High Quality Content by WIKIPEDIA articles! 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 matri...
High Quality Content by WIKIPEDIA articles! 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.
