This function returns the clique complex of a graph $G$. This is the simplicial complex whose faces correspond to the cliques in the graph. That is, $F = \{x_{i_1},...,x_{i_s}\}$ is a face of the clique complex of $G$ if and only if the induced graph on $\{x_{i_1},...,x_{i_s}\}$ is a clique of $G$.
i1 : R = QQ[w,x,y,z]; |
i2 : e = graph {w*x,w*y,x*y,y*z} -- clique on {w,x,y} and {y,z}
o2 = Graph{edges => {{w, x}, {w, y}, {x, y}, {y, z}}}
ring => R
vertices => {w, x, y, z}
o2 : Graph
|
i3 : cliqueComplex e -- max facets {w,x,y} and {y,z}
o3 = | yz wxy |
o3 : SimplicialComplex
|
i4 : g = completeGraph R
o4 = Graph{edges => {{w, x}, {w, y}, {w, z}, {x, y}, {x, z}, {y, z}}}
ring => R
vertices => {w, x, y, z}
o4 : Graph
|
i5 : cliqueComplex g o5 = | wxyz | o5 : SimplicialComplex |
The object cliqueComplex is a method function.