Correlations in spiking neuronal networks with distance dependent connections

Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types.