CompleteGraphQ

CompleteGraphQ[g] yields True if the graph g is a complete graph, and False otherwise.

CompleteGraphQ[g, vlist] yields True if the subgraph induced by vlist is a complete graph.

Examples

Test if a graph is complete:

CompleteGraphQ[CompleteGraph[5]]
(* True *)

A cycle graph is not complete:

CompleteGraphQ[CycleGraph[5]]
(* False *)

Please visit the official Wolfram Language Reference for more details.