Sparse Neural Networks regained attention due to their potential for mathematical and computational advantages. We give motivation to study Artificial Neural Networks (ANNs) from a network science perspective, provide a technique to embed arbitrary Directed Acyclic Graphs into ANNs and report study results on predicting the performance of image classifiers based on the structural properties of the networks' underlying graph. Results could further progress neuroevolution and add explanations for the success of distinct architectures from a structural perspective.