Increased synchrony within neuroanatomical networks is often observed in neurophysiologic studies of human brain disease. Most often, this phenomenon is ascribed to a compensatory process in the face of injury, though evidence supporting such accounts is limited. Given the known dependence of resting-state functional connectivity (rsFC) on underlying structural connectivity (SC), we examine an alternative hypothesis: that topographical changes in SC, specifically particular patterns of disconnection, contribute to increased network rsFC. We obtain measures of rsFC using fMRI and SC using probabilistic tractography in 50 healthy and 28 multiple sclerosis subjects. Using a computational model of neuronal dynamics, we simulate BOLD using healthy subject SC to couple regions. We find that altering the model by introducing structural disconnection patterns observed in those multiple sclerosis subjects with high network rsFC generates simulations with high rsFC as well, suggesting that disconnection itself plays a role in producing high network functional connectivity. We then examine SC data in individuals. In multiple sclerosis subjects with high network rsFC, we find a preferential disconnection between the relevant network and wider system. We examine the significance of such network isolation by introducing random disconnection into the model. As observed empirically, simulated network rsFC increases with removal of connections bridging a community with the remainder of the brain. We thus show that structural disconnection known to occur in multiple sclerosis contributes to network rsFC changes in multiple sclerosis and further that community isolation is responsible for elevated network functional connectivity.