Adding Space to Random Networks of Spiking Neurons: A Method Based on Scaling the Network Size

Many spiking neural network models are based on random graphs that do not include topological and structural properties featured in real brain networks. To turn these models into spatial networks that describe the topographic arrangement of connections is a challenging task because one has to deal with neurons at the spatial network boundary. Addition of space may generate spurious network behavior like oscillations introduced by periodic boundary conditions or unbalanced neuronal spiking due to lack or excess of connections. Here, we introduce a boundary solution method for networks with added spatial extension that prevents the occurrence of spurious spiking behavior. The method is based on a recently proposed technique for scaling the network size that preserves first- and second-order statistics.