# Tree Width of Directed Graph

I'm Nestor Mermoz Thea. I have two definition over the Directed strong pseudoforest and Directed weak pseudoforest that I don't really well understand.

Directed weak pseudoforest: A directed weak pseudoforest is a digraph, in which every weakly connected component contains at most one directed cycle. The class of all directed weak pseudoforests is named DWPF.

Directed strong pseudoforest: A directed strong pseudoforest is a digraph, in which every strongly connected component contains at most one directed cycle, i.e. contains exactly one directed cycle. The class of all directed strong pseudoforests is named DSPF

I have the following questions:

1. What ist the differences between Directed strong pseudoforest and Directed weak pseudoforest?
2. can a pseudoforest have more than one cycle?
3. what mean component in the definition.
4. can I have an Example of Directed weak pseudoforest and Directed strong pseudoforest
• A component of a forest is a tree. Now look up what it means for a tree to be strongly connected. Commented Dec 14, 2022 at 14:44
• I suggest you work through a few examples by hand. Try to find an example with 2 or 3 or 4 vertices of each concept, then try to find an example of a DWPF that is not a DSPF. I expect if you spend a little time you should be able to make some progress on that.
– D.W.
Commented Dec 14, 2022 at 22:28