Brain connectivity networks based on functional magnetic resonance imaging (fMRI) have expanded our understanding of brain functions in both healthy and diseased states. However, most current studies construct connectivity networks using averaged regional time courses with the strong assumption that the activities of voxels contained in each brain region are similar, ignoring their possible variations. Additionally, pairwise correlation analysis is often adopted with more attention to positive relationships, while joint interactions at the network level as well as anti-correlations are less investigated. In this paper, to provide a new strategy for regional activity representation and brain connectivity modeling, a novel homogeneous multiset canonical correlation analysis (HMCCA) model is proposed, which enforces sign constraints on the weights of voxels to guarantee homogeneity within each brain region. It is capable of obtaining regional representative signals and constructing covariation and contravariance networks simultaneously, at both group and subject levels. Validations on two sessions of fMRI data verified its reproducibility and reliability when dealing with brain connectivity networks. Further experiments on subjects with and without Parkinson's disease (PD) revealed significant alterations in brain connectivity patterns, which were further associated with clinical scores and demonstrated superior prediction ability, indicating its potential in clinical practice.