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