Resting state functional brain connectivity networks of single subjects, which connect together correlated brain regions, are usually constructed from functional Magnetic Resonance Imaging (fMRI) data by aggregating variables within predefined brain regions. However, such approaches suffer from loss of relevant information and can lead to incorrect edge identification. We first establish these issues notably stem from the presence of within-region correlations. To alleviate them, and leveraging correlation screening literature, simple and practical characterizations of the mean number of correlation discoveries that flexibly incorporate within-group dependence structures are provided. This novel approach for handling arbitrary within-group correlation is then shown to improve false positive and true positive rates. A novel connectivity network inference framework is then presented. First, inter-regional correlation distribution are estimated. Then, correlation thresholds are constructed for each edge, with false discovery control that can be tailored to one's application. Finally, the proposed framework is implemented on a real-world dataset.