Complete cavity map of the C. elegans connectome

TL;DR

This paper presents the first complete cavity map of the C. elegans neural network, using a novel method to identify higher-order non-trivial cycles, advancing understanding of complex network structures.

Contribution

It introduces a new boundary matrix pruning method to compute higher-order cavities, providing a comprehensive structural map of C. elegans neural network.

Findings

First complete cavity map of C. elegans neural network

Developed a new method for identifying higher-order cycles

Revealed complex higher-order structural features in the network

Abstract

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.