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The neural connectome of the nematode Caenorhabditis elegans has beencompletely mapped, yet in spite of being one of the smallest connectomes (302neurons), the design principles that explain how the connectome structuredetermines its function remain unknown. Here, we find symmetries in thelocomotion neural circuit of C. elegans, each characterized by its own symmetrygroup which can be factorized into the direct product of normal subgroups. Theaction of these normal subgroups partitions the connectome into sectors ofneurons that match broad functional categories. Furthermore, symmetryprinciples predict the existence of novel finer structures inside these normalsubgroups forming feedforward and recurrent networks made of blocks ofimprimitivity. These blocks constitute structures made of circulant matricesnested in a hierarchy of block-circulant matrices, whose functionality isunderstood in terms of neural processing filters responsible for fastprocessing of information.

Symmetry group factorization reveals the structure-function relation in the neural connectome of Caenorhabditis elegans