The extinction of ecosystems and the mechanisms that support or limit species coexistence have long been studied by scientists. It has been shown that competition and cyclic dominance among species promote species coexistence, such as in the classic Rock-Paper-Scissors (RPS) game. However, individuals’ mobility and the underlying topology that defines the neighbourhood relations between individuals also play an important role in maintaining biodiversity. Typically, square grids are used for simulating such interactions. However, these constrain the individuals’ spatial degrees of freedom. In this work, we investigate the effect of the underlying topology on the RPS dynamics. For that purpose, we considered networks with varying node degree distributions and generated according to different theoretical models. We analyzed the time to the first extinction and the patchiness of the in silico ecosystem over time. In general, we observed a distinct large effect of the network topology on the RPS dynamics. Moreover, leaving regular networks aside, the probability of extinction is very high for some network models due to their inherent long-range connections. On the other hand, spatial arrangements characterized by nearest neighbors interactions have fewer long-range correlations, which is essential for biodiversity.