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. 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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