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We apply a network complexity measure to the gap junction network of the somatic nervous system of C. elegans and find that it possesses a much higher complexity than we might expect from its degree distribution alone. This “excess” complexity is seen to be caused by a relatively small set of connections involving command interneurons. We describe a method which progressively deletes these “complexity-causing” connections, and find that when these are eliminated, the network becomes significantly less complex than a random network. Furthermore, this result implicates the previously-identified set of neurons from the synaptic network’s “rich club” as the structural components encoding the network’s excess complexity. This study and our method thus support a view of the gap junction Connectome as consisting of a rather low-complexity network component whose symmetry is broken by the unique connectivities of singularly important rich club neurons, sharply increasing the complexity of the network

Complexity and Vulnerability Analysis of the C. Elegans Gap Junction Connectome