Complete Digraph

Topics: Digraph - Graph Theory

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(definition)

A complete digraph is a digraph where, between every pair of vertices, there exists an arc in both directions. A complete digraph must not have any loops.

A complete digraph is denoted with $D{K}_n$, where $n$ is the number of vertices.

All complete digraphs are symmetric, but not all symmetric digraphs are complete.

Number of Vertices and Arcs §

In a complete digraph with $n$ vertices, there will be $n(n-1)$ arcs.

Every vertex $v$ in a complete digraph will have $d^{-}(v)=n-1=d^{+}(v)$ (see external and internal degrees).