  Neuronal networks constitute a special class of dynamical systems, as they
are formed by individual geometrical components, namely the neurons. In the
existing literature, relatively little attention has been given to the
influence of neuron shape on the overall connectivity and dynamics of the
emerging networks. The current work addresses this issue by considering
simplified neuronal shapes consisting of circular regions (soma/axons) with
spokes (dendrites). Networks are grown by placing these patterns randomly in
the 2D plane and establishing connections whenever a piece of dendrite falls
inside an axon. Several topological and dynamical properties of the resulting
graph are measured, including the degree distribution, clustering coefficients,
symmetry of connections, size of the largest connected component, as well as
three hierarchical measurements of the local topology. By varying the number of
processes of the individual basic patterns, we can quantify relationships
between the individual neuronal shape and the topological and dynamical
features of the networks. Integrate-and-fire dynamics on these networks is also
investigated with respect to transient activation from a source node,
indicating that long-range connections play an important role in the
propagation of avalanches.
