Structual Vulnerability of the Nematode Worm Neural Graph

The number of connected components and the size of the largest connected component are studied under node and edge removal in the connectivity graph of the C. elegans nervous system. By studying the two subgraphs - the directed graph of chemical synapses and the undirected graph of electrical junctions - we observe that adding a small number of undirected edges dramatically reduces the number of components in the complete graph. Under random node and edge removal, the C. elegans graph displays a remarkable structural robustness. We then compare these results with the vulnerability of a number of canonical graph models.