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Network structure or topology is the basis for understanding complex systems.Recently, higher-order structures have been considered as a new researchdirection that can provide new perspectives and phenomena. However, mostexisting studies have focused on simple 1-cycles and triangles, and few haveexplored the higher-order and non-trivial cycles. The current study focused onthe cavity, which is a non-trivial cycle. We proposed a method to computecavities with different orders based on pruning in the boundary matrix andcalculated all cavities of the neural network of Caenorhabditis elegans(\emph{C. elegans}) neural network. This study reports for the first time acomplete cavity map of C. elegans neural network, developing a new method formining higher-order structures that can be applied by researchers inneuroscience, network science and other interdisciplinary fields to explorehigher-order structural markers of complex systems.

Complete cavity map of the C. elegans connectome