Before revision:  We solve analytically a neuronal network model with  binary-state neurons in both random and all-to-all networks . We find strikingly different phase diagrams corresponding to each networkstructure . Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations .
After revision:  We solve analytically a neuronal network model with binary-state neurons in all the network topologies, except ring lattices. Given that apart from network structure, all four models are equivalent, this allows us to understand the role of network structure in neuronal network dynamics. Whilst ER and RR networks are characterized by similar phase diagrams, we find strikingly different phase diagrams corresponding to each networkstructure . Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations .