Given a graph with N nodes and E edges, the task is to count the number of clique having their size as a prime number or prime number of nodes in the given graph.
The word "clique", in its graph-theoretic usage, arose from the work of Luce & Perry (1949), who used complete subgraphs to model cliques (groups of people who all know each other) in social networks. I give you a friendship graph where each vertex corresponds to a person, and there is an edge between two people if they're friends. Sugihara, George (1984), "Graph theory, homology and food webs", in Levin, Simon A.. Tanay, Amos; Sharan, Roded; Shamir, Ron (2002), "Discovering statistically significant biclusters in gene expression data", an offensive content(racist, pornographic, injurious, etc. Paull, M. C.; Unger, S. H. (1959), "Minimizing the number of states in incompletely specified sequential switching functions". Explore anything with the first computational knowledge engine. Contact Us ), "A graph-theoretic definition of a sociometric clique", "Reducibility among combinatorial problems", http://www.cs.berkeley.edu/~luca/cs172/karp.pdf, "Sur le probléme des courbes gauches en Topologie", http://matwbn.icm.edu.pl/ksiazki/fm/fm15/fm15126.pdf, Proceedings of the National Academy of Sciences, http://en.wikipedia.org/w/index.php?title=Clique_(graph_theory)&oldid=499682777. Peay, Edmund R. (1974), "Hierarchical clique structures". Nevertheless, many algorithms for computing cliques have been developed, either running in exponential time (such as the Bron–Kerbosch algorithm) or specialized to graph families such as planar graphs or perfect graphs for which the problem can be solved in polynomial time. Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by Erdős & Szekeres (1935), the term "clique" comes from Luce & Perry (1949), who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other. A windows (pop-into) of information (full-content of Sensagent) triggered by double-clicking any word on your webpage. Kuhl, Crippen & Friesen (1983) use cliques to model the positions in which two chemicals will bind to each other. A graph with 23 1-vertex cliques (its vertices), 42 2-vertex cliques (its edges), 19 3-vertex cliques (the light blue triangles), and 2 4-vertex cliques (dark blue). The red subgraph of the second graph is a clique, but because there is a vertex in the larger graph connected to all 3 vertices in the subgraph, it is not a maximal clique. A maximal clique is a clique that cannot be extended by including one more adjacent vertex, that is, a clique which does not exist exclusively within the vertex set of a larger clique. Choose the design that fits your site. Kuhl, F. S.; Crippen, G. M.; Friesen, D. K. (1983), "A combinatorial algorithm for calculating ligand binding".