The IsClique(G) command returns true if the input graph is a clique (complete graph).  It returns false otherwise.

The IsClique(G, S) command returns true if the collection of vertices S represents a clique in G, and returns false otherwise.

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

$\mathrm{K3}≔\mathrm{CompleteGraph}\left(3\right)$

$\mathrm{K3}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 3\; vertices\; and\; 3\; edge(s)}$

$\mathrm{IsClique}\left(\mathrm{K3}\right)$

$\mathrm{true}$

$\mathrm{C4}≔\mathrm{CycleGraph}\left(4\right)$

$\mathrm{C4}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

$\mathrm{IsClique}\left(\mathrm{C4}\right)$

$\mathrm{false}$

$G≔\mathrm{AddEdge}\left(\mathrm{C4}\,\left\{1\,3\right\}\,\mathrm{inplace}=\mathrm{false}\right)$

$G≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 5\; edge(s)}$

$\mathrm{IsClique}\left(G\,\left[1\,2\,3\right]\right)$

$\mathrm{true}$