  The distribution of the geometric distances of connected neurons is a
practical factor underlying neural networks in the brain. It can affect the
brain\'s dynamic properties at the ground level. Karbowski derived a power-law
decay distribution that has not yet been verified by experiment. In this work,
we check its validity using simulations with a phenomenological model. Based on
the in vitro two-dimensional development of neural networks in culture vessels
by Ito, we match the synapse number saturation time to obtain suitable
parameters for the development process, then determine the distribution of
distances between connected neurons under such conditions. Our simulations
obtain a clear exponential distribution instead of a power-law one, which
indicates that Karbowski's conclusion is invalid, at least for the case of in
vitro neural network development in two-dimensional culture vessels.
