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.
Cite
@article{arxiv.2212.03660,
title = {Complete cavity map of the C. elegans connectome},
author = {Bo Liu and Rongmei Yang and Hao Wang and Linyuan Lü},
journal= {arXiv preprint arXiv:2212.03660},
year = {2022}
}