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    Complete Graph

    Alternate names

    fully connected graph | fully connected network | universal graph

    Basic definition

    A complete graph is a network in which every pair of vertices is connected by an edge.

    Detailed definition

    A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and has (n 2) = n(n - 1)/2 (the triangular numbers) undirected edges, where (n k) is a binomial coefficient. In older literature, complete graphs are sometimes called universal graphs. The complete graph K_n is also the complete n-partite graph K_(n×1) = K_(1, ..., 1_︸_n).

    Related terms

    barbell graph | clique | complete bipartite graph | complete digraph | complete k-partite graph | empty graph | graph complement | Guy's conjecture | lollipop graph | odd graph | regular polygon division by diagonals | singleton graph

    Educational grade level

    college level

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