Editing Graph (discrete mathematics) (section)

=== Mixed graph ===
{{main|Mixed graph}}
[[File:Example of simple mixed graph.jpg|thumb|upright|A mixed graph with three vertices, two directed edges, and an undirected edge.]]

A ''mixed graph'' is a graph in which some edges may be directed and some may be undirected. It is an ordered triple {{math|1=''G'' = (''V'', ''E'', ''A'')}} for a ''mixed simple graph'' and {{math|1=''G'' = (''V'', ''E'', ''A'', ''ϕ{{sub|E}}'', ''ϕ{{sub|A}}'')}} for a ''mixed multigraph'' with {{mvar|V}}, {{mvar|E}} (the undirected edges), {{mvar|A}} (the directed edges), {{mvar|ϕ{{sub|E}}}} and {{mvar|ϕ{{sub|A}}}} defined as above. Directed and undirected graphs are special cases.