In a Graph of Vertices, a subset of pairwise adjacent Vertices is known as a clique. A clique is a fully connected subgraph of a given graph. The problem of finding the size of a clique for a given Graph is an NP-Complete Problem. The number of graphs on nodes having 3 cliques are 0, 0, 1, 4, 12, 31, 67, ... (Sloane's A005289).
See also Clique Number, Maximum Clique Problem, Ramsey Number, Turán's Theorem
Sloane, N. J. A. Sequence
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.