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Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain and edges representing the strength of connectivity between these locations. One challenge in analyzing such data is that inference at the individual edge level is not particularly biologically meaningful; interpretation is more useful at the level of so-called functional systems or groups of nodes and connections between them; this is often called “graph-aware” inference in the neuroimaging literature. However, pooling over functional regions leads to significant loss of information and lower accuracy. Another challenge is correlation among edge weights within a subject which makes inference based on independence assumptions unreliable. We address both of these challenges with a linear mixed effects model, which accounts for functional systems and for edge dependence, while still modeling individual edge weights to avoid loss of information. The model allows for comparing two populations, such as patients and healthy controls, both at the functional regions level and at individual edge level, leading to biologically meaningful interpretations. We fit this model to resting state fMRI data on schizophrenic patients and healthy controls, obtaining interpretable results consistent with the schizophrenia literature.