The default mode network (DMN) comprises brain structures maximally active at rest. Disturbance of network nodes or their connections occurs with some neuropsychiatric conditions and may underlie associated dysfunction. DMN connectivity has not been examined in alcoholism, which is marked by compromised DMN nodes and impaired spatial working memory. To test whether performance would be related to DMN integrity, we examined DMN functional connectivity using functional magnetic resonance imaging (fMRI) data and graph theory analysis. We assumed that disruption of short paths between network nodes would attenuate processing efficiency. Alcoholics and controls were scanned at rest and during a spatial working memory task. At rest, the spontaneous slow fluctuations of fMRI signals in the posterior cingulate and cerebellar regions in alcoholics were less synchronized than in controls, indicative of compromised functional connectivity. Graph theory analysis indicated that during rest, alcoholics had significantly lower efficiency indices than controls between the posterior cingulate seed and multiple cerebellar sites. Greater efficiency in several connections correlated with longer sobriety in alcoholics. During the task, on which alcoholics performed on par with controls, connectivity between the left posterior cingulate seed and left cerebellar regions was more robust in alcoholics than controls and suggests compensatory networking to achieve normal performance.