Clique complex

The clique complex of a graph. Cliques of size one are shown as small red disks; cliques of size two are shown as black line segments; cliques of size three are shown as light blue triangles; and cliques of size four are shown as dark blue tetrahedra.

Clique complexes, independence complexes, flag complexes, Whitney complexes and conformal hypergraphs are closely related mathematical objects in graph theory and geometric topology that each describe the cliques (complete subgraphs) of an undirected graph.