# 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.
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).