TITLE: How do you correctly reason that this directed graph is acyclic?
QUESTION [29 upvotes]: How can you correctly reason that this directed graph is acyclic?


I can only visually say that this graph is acyclic because there is not a single path in the graph where the starting vertex is equal to the ending vertex. But is this actually a reason you can say if someone asks you?
Is there maybe some kind of rule / formula where you can determine this by comparing the amount of vertices with the amount of edges?
We have here $6$ vertices and $10$ edges.
I hope you can give me some help because if someone asks me why this directed graph or generally a directed graph is acyclic, I would go like that here and I don't feel good about it.

REPLY [2 votes]: The adjacency matrix of the graph to the power of the number of vertices is the zero matrix...
 In particular, all eigenvalues of the adjacency matrix are zero...