The connectivity analysis is a powerful technique for investigating a hard-wired brain architecture as well as flexible, functional dynamics tied to human cognition. Recent multi-modal connectivity studies had the challenge of combining functional and structural connectivity information into one integrated network. In this paper, we proposed a simplex regression model with graph-constrained Elastic Net (GraphNet) to estimate functional networks enriched by structural connectivity in a biologically meaningful way with a low model complexity. Our model constructed the functional networks using sparse simplex regression framework and enriched structural connectivity information based on GraphNet constraint. We applied our model on the real neuroimaging datasets to show its ability for predicting a clinical condition. Our results demonstrated that integrating multi-modal features could detect more sensitive and subtle brain biomarkers than using a single modality.