# What is the difference between directed graph and bidirectional graph?

Is the graph above bidirectional? The image in wikipedia confused me a lot, before I heard about something called as bidirectional graph, I would say the above one a directed graph, but I am not sure now.

– D.W.
Jan 6 at 9:05

As stated in the Wikipedia article, a bidirected graph is a graph where all edges have an orientation at both edges of the edge. The orientation is an arrow head. So in your example, it is not a bidirected graph because the edges only have orientation on one end.

The following would be an example of a bidirected graph. Notice there is an arrow head on both sides of each edge of the graph.

There are three types of edges of a bidirected graph.

1. Extroverted edge: arrow heads oriented outwards or towards vertices (e.g. $$\{a,b\}$$)
2. Introvert edge: arrow heads oriented inwards or away from vertices (e.g. $$\{b,c\}$$)
3. Directed edge: arrow heads oriented in one direction or away from one vertex and towards the other (e.g. $$\{a,c\}$$)

There are also loose edges (which have no orientation on either end) and half edges (which have orientation on one end).

Another use of bidirected graph is a directed graph where each edge has a matching edge going the opposite direction. Your example would not be a bidirected graph in this context either since there are edges that do not have the reverse direction (e.g. $$(1,3)$$ exists but $$(3,1)$$ does not). The following is an example of bidirected graph in this context.

Bidirected graphs are not common in my experience. This is just from a quick read of the Wiki article.

1. Bidirected graphs: https://en.wikipedia.org/wiki/Bidirected_graph
2. Directed graphs: https://en.wikipedia.org/wiki/Directed_graph

I would suggest you look at the wikipedia article for bidirected graphs. It states that directed graphs is a special kind of bidirected graph. There are introverted edges, extraverted edges, and directed. They aren’t different but one is a subset of the other.

You can think of a directed edge as a one way street while a uni/bi directed is a 2 way street. A uni/bi directed graph is basically a graph with only two way streets while a directed graph can have one way streets too.

• I can only regard directed/bidirected edges as one/two-way streets. The OP asks for directed/bidirected graphs. Jan 6 at 1:47