# 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.

• The question says "Wikipedia" but the link is not to Wikipedia. The Wikipedia link is en.wikipedia.org/wiki/Bidirected_graph. The question seems to be answered suitably at Wikipedia; I'm not sure what prevents you from answering the question on your own, after reading Wikipedia. Wikipedia also has references where you can read more if you don't understand. The link you provide talks about "bidirected" but your question asks about "bidirectional". Which do you want to know about?
– D.W.
Commented Jan 6, 2021 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. Commented Jan 6, 2021 at 1:47

there are some mathematic concepts i think may useful for you. first, the picture you show above is a directed graph. the difference between bidirected graph and directed graph is that each node in bidirected graph have two side: VdX{left,right}, and each edge on bidirected graph is pair of two side, and every endpoint the edge will have information about which side of the node it connected to.

picture A is a directed graph. each edge only have one direction. picture B is a bidirected graph, each endpoint of edge is connected to a specific side of node. reference doi: 10.1089/cmb.2017.0251

Arrows are there to indicate which is the traversal direction. [Directed]

No arrows implicitly mean that both directions can be taken. [Bidirectional or undirected]

IMO, a graph where every arrow has the reverse counterpart could be considered both as a directed or undirected graph (depending on context).