Symmetric Digraph

Topics: Digraph - Graph Theory

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(definition)

A symmetric digraph is a digraph where, for every connected pair of vertices $(v_i,v_j)$, there exists an arc that goes $v_i\to v_j$ and another one that goes $v_j\to v_i$ (i.e. a pair of recurring arcs).

Complete vs. Symmetric

A complete digraph is very similar to a symmetric digraph. The difference is that a complete digraph contains a pair of recurring arcs between every pair of vertices, but a symmetric digraph only contains a pair of recurring arcs where a connection already exists.

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