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Graph Eigenvalue


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

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References

Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, 1993.Cvetković, D. M.; Doob, M.; and Sachs, H. Spectra of Graphs: Theory and Applications, 3rd rev. enl. ed. New York: Wiley, 1998.Cvetković, D.; Rowlinson, P.; and Simić, S. Spectral Generalizations of Line Graphs: On Graphs With Least Eigenvalue −2. Cambridge, England: Cambridge University Press, 2004.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 85, 1990.

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Graph Eigenvalue

Cite this as:

Weisstein, Eric W. "Graph Eigenvalue." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphEigenvalue.html

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