Aphasia is one of the most prevalent cognitive syndromes caused by stroke. The rarity of premorbid imaging and heterogeneity of lesion size and extent obfuscates the links between the local effects of the lesion, global anatomical network organization, and aphasia symptoms. We applied a simulated attack approach to examine the effects of 39 stroke lesions on network topology by simulating their effects in a control sample of 36 healthy brain networks. We focused on measures of global network organization thought to support overall brain function and resilience in the whole brain and within the left hemisphere. After removing lesion volume from the network topology measures and behavioral scores (the Western Aphasia Battery Aphasia Quotient; WAB-AQ), four behavioral factor scores obtained from a neuropsychological battery, and a factor sum), we compared the behavioral variance accounted for by simulated post-stroke connectomes to that observed in the randomly permuted data. Overall, global measures of network topology in the whole brain and left hemisphere accounted for 10% variance or more of the WAB-AQ and the lexical factor score beyond lesion volume and null permutations. Streamline networks provided more reliable point estimates than FA networks. Edge weights and network efficiency were weighted most highly in predicting the WAB-AQ for FA networks. Overall, our results suggest that global network measures can provide modest statistical value predicting overall aphasia severity, but less value in predicting specific behaviors. Variability in estimates could be induced by premorbid ability, deafferentation and diaschisis, and neuroplasticity following stroke.