A major objective of brain science research is to model and quantify functional interaction patterns among neural networks, in the sense that meaningful interaction patterns reflect the working mechanisms of neural systems and represent their relationships with the external world. Most current research approaches in the neuroimaging field, however, focus on pair-wise functional/effective connectivity and are thus unable to handle high-order, network-scale functional interactions. In this paper, we propose a novel structurally-weighted LASSO (SW-LASSO) regression model to represent the functional interaction among multiple regions of interests (ROIs) based on resting state fMRI (rsfMRI) data. In particular, the structural connectivity constraints derived from diffusion tenor imaging (DTI) data are used to guide the selection of the weights, thus adaptively adjusting the penalty levels of different coefficients which correspond to different ROIs. The robustness and accuracy of our models are evaluated and demonstrated via a series of carefully designed experiments. In an application example, the generated regression graphs show different assortative mixing patterns between Mild Cognitive Impairment (MCI) patients and normal controls (NC). Our results indicate that the proposed model has promising potential to enable the construction of high-order functional networks and their applications in clinical datasets.