Uniform random sparse network architectures are ubiquitous in computational neuroscience, but the implicit hypothesis that they are a good representation of real neuronal networks has been met with skepticism. Here we used two experimental data sets, a study of triplet connectivity statistics and a data set measuring neuronal responses to channelrhodopsin stimuli, to evaluate the fidelity of thousands of model networks. Network architectures comprised three neuron types (excitatory, fast spiking, and nonfast spiking inhibitory) and were created from a set of rules that govern the statistics of the resulting connection types. In a high-dimensional parameter scan, we varied the degree distributions (i.e., how many cells each neuron connects with) and the synaptic weight correlations of synapses from or onto the same neuron. These variations converted initially uniform random and homogeneously connected networks, in which every neuron sent and received equal numbers of synapses with equal synaptic strength distributions, to highly heterogeneous networks in which the number of synapses per neuron, as well as average synaptic strength of synapses from or to a neuron were variable. By evaluating the impact of each variable on the network structure and dynamics, and their similarity to the experimental data, we could falsify the uniform random sparse connectivity hypothesis for 7 of 36 connectivity parameters, but we also confirmed the hypothesis in 8 cases. Twenty-one parameters had no substantial impact on the results of the test protocols we used.