Neuroimaging studies of cognitive control have identified two distinct networks with dissociable resting state connectivity patterns. This study, in patients with heterogeneous damage to these networks, demonstrates network independence through a double dissociation of lesion location on two different measures of network integrity: functional correlations among network nodes and within-node graph theory network properties. The degree of network damage correlates with a decrease in functional connectivity within that network while sparing the nonlesioned network. Graph theory properties of intact nodes within the damaged network show evidence of dysfunction compared with the undamaged network. The effect of anatomical damage thus extends beyond the lesioned area, but remains within the bounds of the existing network connections. Together this evidence suggests that networks defined by their role in cognitive control processes exhibit independence in resting data.