We seek to understand how certain characteristics in the structure of neuron-to-neuron connectivity shape the activity of local neural circuits. The local connectivity of cortical networks features a nonrandom higher order structure characterized by the presence of tightly connected clusters of neurons. We use a biologically detailed model of neocortical microcircuitry that recreates these features and simplify its complexity algorithmically while preserving the larger scale connectivity trends. We then simulate spontaneous and evoked activity in the two models with simplified and complex connectivity and compare the resulting spiking statistics. The results allow us to characterize the role of the higher level structure of connectivity in interaction with other biological features shaping neuronal activity such as synaptic adaptation and noise.