Elucidating the coupling between the structure and the function of the brain and its development across maturation has attracted a lot of interest in the field of network neuroscience in the last fifteen years. Mounting evidence support the hypothesis that the interplay between the structural architecture and the functional processes of the brain plays an important role in the onset of certain brain disorders such as schizophrenia and autism. This papers introduces a method called NBS-SNI that integrates both representations into a single framework, and identifies connectivity abnormalities in case-control studies. With this method, significance is given to the properties of the nodes, as well as to the connections between them. This approach builds on the well-established Network-based statistics (NBS) proposed in 2010. We uncover and identify the regimes in which NBS-SNI offers a gain in statistical resolution to identify a contrast of interest using synthetic data. We also apply our method on a real case-control study of individuals diagnosed with autism. Using NBS-SNI and node properties such as the closeness centrality and local information dimension, we found both hypo and hyperconnected subnetworks and show that our method can offer a 9 percentage points gain in prediction power over the standard NBS.