The spectrum of a graph G is the set of the eigenvalues of the adjacency matrix A corresponding to G. For simple graphs, these eigenvalues are all real since A must be symmetric. The user should be aware that Macaulay 2 does not give exact values for these eigenvalues, they are numerical approximations, but it is still a good tool to use to check if two graphs are isomorphic; isomorphic graphs share the same spectrum although the converse is not necessarily true.
i1 : spectrum completeGraph 6
o1 = {-1, -1, -1, -1, -1, 5}
o1 : List
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i2 : spectrum graphLibrary "petersen"
o2 = {-2, -2, -2, -2, 1, 1, 1, 1, 1, 3}
o2 : List
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The object spectrum is a method function.