The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix . The set of eigenvalues of a graph is called a graph spectrum .
The largest eigenvalue absolute value in a graph is called the spectral radius of the graph, and the second smallest eigenvalue of the Laplacian matrix of a graph is called its algebraic connectivity . The sum of absolute values of graph eigenvalues is called the graph energy .
See also Algebraic Connectivity ,
Characteristic Polynomial ,
Cospectral Graphs ,
Graph Energy ,
Graph Spectrum ,
Spectral Radius Explore with Wolfram|Alpha References Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cvetković, D. M.; Doob, M.; and Sachs, H. Spectra of Graphs: Theory and Applications, 3rd rev. enl. ed. Cvetković, D.; Rowlinson, P.; and Simić, S. Spectral Generalizations of Line Graphs: On Graphs With Least Eigenvalue −2. Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Referenced on Wolfram|Alpha Graph Eigenvalue Cite this as: Weisstein, Eric W. "Graph Eigenvalue." From MathWorld https://mathworld.wolfram.com/GraphEigenvalue.html
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