A clique of a graph is a subset of its vertices which induces a complete subgraph. That is, a set of vertices is a clique if every pair of vertices in the set forms an edge of the graph. This function returns all cliques of a specified size, and if no size is given, it returns all cliques. Note that all the edges of the graph are considered cliques of size two.
i1 : R = QQ[a..d]; |
i2 : G = completeGraph R
o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}}}
ring => R
vertices => {a, b, c, d}
o2 : Graph
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i3 : getCliques(G,3)
o3 = {{a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}}
o3 : List
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i4 : getCliques(G,4)
o4 = {{a, b, c, d}}
o4 : List
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i5 : getCliques G
o5 = {{a, b}, {a, c}, {b, c}, {a, d}, {b, d}, {c, d}, {a, b, c}, {a, b, d},
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{a, c, d}, {b, c, d}, {a, b, c, d}}
o5 : List
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The object getCliques is a method function.