I want to evaluate some algorithms for the directed graph classification task. Therefore, I'm looking for directed graphs data sets (preferably without node or edge features) as benchmarks. Do you have any ideas for datasets that could fit?
In Chapter 11 - Transitivity, structural, balance, and hierarchy, of the free online book Methods for Network Analysis, there is a picture how triads of nodes are be classified. Scroll down to section "11.4 - Calculating a triad census" to see the figure and the names that I mean.
(the first part, the number before the "-" is a counter.)
Obviously, this classification is different from a machine-learning classification (=prediction) task.
However, if ML classification is your use-case, then I have no dataset examples. But the book in the same chapter, but section "11.5 - Random graphs galore!" also shows how you can create your own synthetic directed graphs with R and igraph.
Then you can control and know the size and the properties of the graph in advance. Perfect for prediction tasks and algorithm evaluation!