The brain connectome provides an unprecedented degree of information about the organization of neuronal network architecture, both at a regional level, as well as regarding the entire brain network. Over the last several years the neuroimaging community has made tremendous advancements in the analysis of structural connectomes derived from white matter fiber tractography or functional connectomes derived from time-series blood oxygen level signals. However, computational techniques that combine structural and functional connectome data to discover complex relationships between fiber density and signal synchronization, including the relationship with health and disease, has not been consistently performed. To overcome this shortcoming, a novel connectome feature selection technique is proposed that uses hypergraphs to identify connectivity relationships when structural and functional connectome data is combined. Using publicly available connectome data from the UMCD database, experiments are provided that show SVM classifiers trained with structural and functional connectome features selected by our method are able to correctly identify autism subjects with 88 % accuracy. These results suggest our combined connectome feature selection approach may improve outcome forecasting in the context of autism.