Networks of random trees as a model of neuronal connectivity

We provide an analysis of a randomly grown 2-d network which models the morphological growth of dendritic and axonal arbors. From the stochastic geometry of this model we derive a dynamic graph of potential synaptic connections. We estimate standard network parameters such as degree distribution, average shortest path length and clustering coefficient, considering all these parameters as functions of time. Our results show that even a simple model with just a few parameters is capable of representing a wide spectra of architecture, capturing properties of well-known models, such as random graphs or small world networks, depending on the time of the network development. The introduced model allows not only rather straightforward simulations but it is also amenable to a rigorous analysis. This provides a base for further study of formation of synaptic connections on such networks and their dynamics due to plasticity.