From Density to Void: Why Brain Networks Fail to Reveal Complex Higher-Order Structures

In brain network analysis using resting-state fMRI, there is growing interest in modeling higher-order interactions beyond simple pairwise connectivity via persistent homology. Despite the promise of these advanced topological tools, robust and consistently observed higher-order interactions over time remain elusive. In this study, we investigate why conventional analyses often fail to reveal complex higher-order structures - such as interactions involving four or more nodes - and explore whether such interactions truly exist in functional brain networks. We utilize a simplicial complex framework often used in persistent homology to address this question.