Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease, characterized by progressive loss of motor function. While the pathogenesis of ALS remains largely unknown, recent histological examinations of Brettschneider and colleagues have proposed four time-sequential stages of neuropathology in ALS based on levels of phosphorylated 43. kDa TAR DNA-binding protein (pTDP-43) aggregation. What governs dissemination of these aggregates between segregated regions of the brain is unknown. Here, we cross-reference stages of pTDP-43 pathology with in vivo diffusion weighted imaging data of 215 adult healthy control subjects, and reveal that regions involved in pTDP-43 pathology form a strongly interconnected component of the brain network (p = 0.04) likely serving as an anatomical infrastructure facilitating pTDP-43 spread. Furthermore, brain regions of subsequent stages of neuropathology are shown to be more closely interconnected than regions of more distant stages (p = 0.002). Computational simulation of disease spread from first-stage motor regions across the connections of the brain network reveals a pattern of pTDP-43 aggregation that reflects the stages of sequential involvement in neuropathology (p = 0.02), a pattern in favor of the hypothesis of pTDP-43 pathology to spread across the brain along axonal pathways. Our findings thus provide computational evidence of disease spread in ALS to be directed and constrained by the topology of the anatomical brain network.