In this paper, we investigate the impact of neural networks (NNs) topology on adversarial robustness. Specifically, we study the graph produced when an input traverses all the layers of a NN, and show that such graphs are different for clean and adversarial inputs. We find that graphs from clean inputs are more centralized around highway edges, whereas those from adversaries are more diffuse, leveraging under-optimized edges. Through experiments on a variety of datasets and architectures, we show that these under-optimized edges are a source of adversarial vulnerability and that they can be used to detect adversarial inputs.