The ability to detect an unusual concentration of extreme observations in a connected region of a graph is fundamental in a number of use cases, ranging from traffic accident detection in road networks to intrusion detection in computer networks. This task is usually performed using scan statistics-based methods, which require explicitly finding the most anomalous subgraph and thus are computationally intensive. We propose a more scalable method in the case where the observations are assigned to the edges of a large-scale network. The rationale behind our work is that if an anomalous cluster exists in the graph, then the subgraph induced by the most individually anomalous edges should contain an unexpectedly large connected component. We therefore reformulate our problem as the detection of anomalous sample paths of a percolation process on the graph, and our contribution can be seen as a generalization of previous work on percolation-based cluster detection. We evaluate our method through extensive simulations.