  Probing the developing neural circuitry in Caenorhabditis elegans has
enhanced our understanding of nervous systems. The C. elegans connectome, like
those of other species, is characterized by a rich club of densely connected
neurons embedded within a small-world architecture. This organization of
neuronal connections, captured by quantitative network statistics, provides
insight into the system's capacity to perform integrative computations. Yet
these network measures are limited in their ability to detect weakly connected
motifs, such as topological cavities, that may support the systems capacity to
perform segregated computations. We address this limitation by using persistent
homology to track the evolution of topological cavities in the growing C.
elegans connectome throughout neural development, and assess the degree to
which the growing connectomes topology is resistant to biological noise. We
show that the developing connectome topology is both relatively robust to
changes in neuron birth times and not captured by similar growth models.
Additionally, we quantify the consequence of a neurons specific birth time and
ask if this metric tracks other biological properties of neurons. Our results
suggest that the connectomes growing topology is a robust feature of the
developing connectome that is distinct from other network properties, and that
the growing topology is particularly sensitive to the exact birth times of a
small set of predominantly motor neurons. By utilizing novel measurements that
track biological features, we anticipate that our study will be helpful in the
construction of more accurate models of neuronal development in C. elegans
