Abstract Measuring differences among complex networks is a well-studied research topic. Particularly, in the context of brain networks, there are several proposals. Nevertheless, most of them address the problem considering unweighted networks. Here, we propose a metric based on modularity and Jaccard index to measure differences among brain-connectivity weighted networks built from diffusion-weighted magnetic resonance data. We use a large dataset to test our metric: a synthetic Ground Truth network (GT) and a set of networks available from a tractography challenge, three sets computed from GT perturbations, and a set of classic random graphs. We compare the performance of our proposal with the most used methods as Euclidean distance between matrices and a kernel-based distance. Our results indicate that the proposed metric outperforms those previously published distances. More importantly, this work provides a methodology that allows differentiating diverse groups of graphs based on their differences in topological structure.