Simplicial sets | Graph theory | Simplicial homology

Independence complex

The independence complex of a graph is a mathematical object describing the independent sets of the graph. Formally, the independence complex of an undirected graph G, denoted by I(G), is an abstract simplicial complex (that is, a family of finite sets closed under the operation of taking subsets), formed by the sets of vertices in the independent sets of G. Any subset of an independent set is itself an independent set, so I(G) is indeed closed under taking subsets. Every independent set in a graph is a clique in its complement graph, and vice versa. Therefore, the independence complex of a graph equals the clique complex of its complement graph, and vice versa. (Wikipedia).

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Related pages

Abstract simplicial complex | Clique (graph theory) | Independent set (graph theory) | Rainbow-independent set | Induced matching | Bipartite graph | Homological connectivity | Chordal graph | Line graph | Complement graph | Meshulam's game | Matching (graph theory) | Clique complex | Dominating set | Reduced homology