This is similar to this question: Can someone explain in simple terms to me what a Directed acyclic graph is?. However I would like to receive similar answers about an acyclic graph (i.e. not necessarily directed).
Does the fact that it's nondirected change the "shapes" that a nondirected acyclic graph can make? Or could it make the exact same shapes as a directed acyclic graph?
A little research into graph theory and I found this: Forests!
I'm not going to pretend I know much about graph theory, but I think there are some good explanations out there which I'll link below.
Basically, it's two 'Tree' graphs that do not intertwine, becoming a non-directed forest as opposed to a single entity.
The term "Undirected Acyclic Graph" is never used, because it is exactly equivalent to Forests (i.e., forests are not just an example of "Undirected Acyclic Graphs" - they are exactly the "Undirected Acyclic Graphs").
This can easily be seen if you look at the definition of a tree (or, by extension, a forest): "In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any acyclic connected graph is a tree." (from the Wikipedia entry on Trees)
If you now drop the requirement that the graph must be connected you go from trees to forests, resulting in "any acyclic graph is a forest".
A "Directed Acyclic Graph" or a DAG is a graph where each edge (u, v) for two vertices points in a certain direction and there are no cycles. It is proven that there is always at least one vertex that does not have incoming edges.
A "Undirected Acyclic Graph" is considered a tree if connected and a forest if one or more of its "branches" is disconnected.
Both graphs can assemble different shapes. The shapes of DAGs are usually based on their ordering. The shape of Undirected acyclic graphs are based on the connectivity of the branches. The two graphs can assemble the same or similar shape based on these parameters.
