By taking advantage of spatially explicit modelling and network analysis, we investigated how species–area relationships (SARs) emerge and are maintained by dispersal and how the spatial arrangement of islands affects colonization/extinction dynamics of SARs. In particular, we generated different archipelagos characterized by varying geometric properties and then we simulated inter-island dispersal/colonization patterns. As the model proceeds through time, species accumulate on different islands according to their dispersal ability and depending on island size and isolation. During each time step, the model fit a power function that thus enabled us to track the emergence of island SARs (ISARs). After equilibrium was reached, we simulated a phase of reduced dispersal. Each simulated archipelago was analysed as a network in which each island was a node connected to other nodes (islands) based on pairwise spatial distances. We found that basic properties of the underlying connectivity network were correlated with ISAR properties, although the best predictor of richness was almost always island area. In nearly all simulations, the ISAR weakened after reducing the dispersal ability of the species. Our study demonstrates that a spatially explicit dispersal simulation model and network analysis can provide meaningful insight into the evolution and robustness of ISARs.