Abstract : Current studies of cortical network dynamics are usually based on purely random wiring. Generally, these studies are focused on a local scale, where about 10 percent of all possible connections are realized. Neuronal connections in the cortex, however, show a more complex spatial pattern composed of local and long-range patchy connections. Here, we ask to what extent the assumption of such specific geometric traits influences the resulting dynamical behavior of network models. Analyzing the characteristic measures describing spiking neuronal networks (e.g., firing rate, coefficient of variation, correlation coefficient), we ascertain and compare the dynamical state spaces of different types of networks. To include long-range connections, we enlarge the spatial scale, resulting in a much sparser connectivity than what is usually assumed. Similar to previous studies, we can distinguish between different dynamical states (e.g., synchronous regular firing), depending on the external input rate and the numerical relation between excitatory and inhibitory synaptic weights. Yet, local couplings in such very sparsely connected networks seem to induce specific correlations and require another regularity measure than the coefficient of variation.