Before revision:  Apart from the classical random graph families including random, scale-free and small world graphs, we introduced a novel and flexible algorithm for directly generating random directed acyclic graphs (DAG) and studied a class of graphs derived from functional resting state fMRI networks. A majority of the best performing networks were indeed in these new families. We also proposed a general procedure for turning a graph into a DAG necessary for a feed-forward neural network. We investigated various structural and numerical properties of the graphs in relation to neural network test accuracy.
After revision:  We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy.