Landscapes are increasingly fragmented, and conservation programs have started to look at network approaches for maintaining populations at a larger scale. We present an agent-based model of predator–prey dynamics where the agents (i.e. the individuals of either the predator or prey population) are able to move between different patches in a landscaped network. We then analyze population level and coexistence probability given node-centrality measures that characterize specific patches. We show that both predator and prey species benefit from living in globally well-connected patches (i.e. with high closeness centrality). However, the maximum number of prey species is reached, on average, at lower closeness centrality levels than for predator species. Hence, prey species benefit from constraints imposed on species movement in fragmented landscapes since they can reproduce with a lesser risk of predation, and their need for using anti-predatory strategies decreases