Before revision:  Since none of the classical numerical graph invariants by itself seems to allow to single out the best networks , we introduced new numerical characteristics that selected a set of quasi-1-dimensional graphs, which were the majority among the best performing networks. 
After revision:  Since none of the classical numerical graph invariants by itself seems to allow to single out the best networks . Consequently, we introduce a new numerical graph characteristic that selects a set of quasi-1-dimensional graphs, which were the majority among the best performing networks.