  In the past two decades, significant advances have been made in understanding
the structural and functional properties of biological networks, via
graph-theoretic analysis. In general, most graph-theoretic studies are
conducted in the presence of serious uncertainties, such as major undersampling
of the experimental data. In the specific case of neural systems, however, a
few moderately robust experimental reconstructions do exist, and these have
long served as fundamental prototypes for studying connectivity patterns in the
nervous system. In this paper, we provide a comparative analysis of these
"historical" graphs, both in (unmodified) directed and (often symmetrized)
undirected forms, and focus on simple structural characterizations of their
connectivity. We find that in most measures the networks studied are captured
by simple random graph models; in a few key measures, however, we observe a
marked departure from the random graph prediction. Our results suggest that the
mechanism of graph formation in the networks studied is not well-captured by
existing abstract graph models, such as the small-world or scale-free graph.
