The SeidelSpectrum command returns the Seidel spectrum of the eigenvalues of a specified graph. That is the set of eigenvalues of the matrix $J-\mathrm{I}-2A$ where $J$ is the all-one matrix, $\mathrm{I}$ is the identity matrix and $A$ is the adjacency matrix of the graph. The output is a list $L$. Each element of $L$ is a list of size 2, where the first element is an eigenvalue and the second element is its multiplicity.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$G≔\mathrm{ClebschGraph}\left(\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 16\; vertices\; and\; 40\; edge(s)}$

$\mathrm{SeidelSpectrum}\left(G\right)$

$\left[\left[\mathrm{-3}\,10\right]\,\left[5\,6\right]\right]$

$P≔\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{SeidelSpectrum}\left(P\right)$

$\left[\left[\mathrm{-3}\,5\right]\,\left[3\,5\right]\right]$