Graph Theory has spread across different domains due to its ability to capture and exploit information about the interactions among elements. One of the most promising applications relies on the area of Neuroscience, where the exploration of brain connectivity (BC) has become a topic of major interest. In this context, we introduce a new framework to extract and analyze BC data for detecting disrupted connectivity subnetworks associated with neurodegenerative disorders. Our framework conceptualizes the problem of identifying connectivity subnetworks as an optimization, and leverages the potential of Machine Learning techniques to optimize the objective function. We applied this methodology to 18F-fluorodeoxyglucose positron emission tomography (FDG-PET) data from patients with primary progressive aphasia (PPA), a neurodegenerative syndrome characterized by three distinct clinico-pathological variants featuring diverse topographical and horological patterns. Our findings showed that the proposed approach detects impaired BC subnetworks associated with the characteristic fingerprints of the disease. This methodology offers a fresh perspective on studying BC, complementing conventional approaches based on Graph Theory.