Studying patterns of parasite local adaptation can provide insights into the spatiotemporal dynamics of host-parasite coevolution. Many factors, both biotic and abiotic, have been identified that influence parasite local adaptation. In particular, dispersal and population structuring are considered important determinants of local adaptation. We investigated how the shape of the spatial dispersal network within experimental landscapes affected local adaptation of a bacteriophage parasite to its bacterial host. Regardless of landscape topology, dispersal always led to the evolution of phages with broader infectivity range. However, when the spatial dispersal network resulted in spatial variation in the breadth of phage infectivity range, significant levels of parasite local adaptation and local maladaptation were detected within the same landscape using the local versus foreign definition of local adaptation. By contrast, local adaptation was not detected using the home versus away or local versus global definitions of local adaptation. This suggests that spatial dispersal networks may play an important role in driving parasite local adaptation, particularly when the shape of the dispersal network generates nonuniform levels of host resistance or parasite infectivity throughout a species' range.