This technology introduces two novel functional connectivity (FC) estimation methods—a Log-Regularized Laplacian Graph estimator and a K-Nearest Neighbors (KNN) Graph estimator—that generate sparse FC matrices from resting-state fMRI BOLD time series. By pruning weak and irrelevant connections, these methods reduce noise and computational complexity in graph construction and downstream machine learning tasks. Validated against eight existing estimators using Human Connectome Project data, the sparse FCs reveal clearer modular brain structures and achieve superior computational efficiency, making them valuable tools for neuroimaging studies.