  We show that in model neuronal cultures, where the probability of
interneuronal connection formation decreases exponentially with increasing
distance between the neurons, there exists a small number of spatial nucleation
centers of a network spike, from where the synchronous spiking activity starts
propagating in the network typically in the form of circular traveling waves.
The number of nucleation centers and their spatial locations are unique and
unchanged for a given realization of neuronal network but are different for
different networks. In contrast, if the probability of interneuronal connection
formation is independent of the distance between neurons, then the nucleation
centers do not arise and the synchronization of spiking activity during a
network spike occurs spatially uniform throughout the network. Therefore one
can conclude that spatial proximity of connections between neurons is important
for the formation of nucleation centers. It is also shown that fluctuations of
the spatial density of neurons at their random homogeneous distribution typical
for the experiments $\textit{in vitro}$ do not determine the locations of the
nucleation centers. The simulation results are qualitatively consistent with
the experimental observations.
