Higher-Order Interactions in Brain Connectomics: Implicit versus Explicit Modeling Approaches

Abstract: The human brain is a complex system defined by multi-way, higher-order interactions invisible to traditional pairwise network models. Although a diverse array of analytical methods has been developed to address this shortcoming, the field remains fragmented, lacking a unifying conceptual framework that integrates and organizes the rapidly expanding methodological landscape of higher-order brain connectivity. This review provides a synthesis of the methodologies for studying higher-order brain connectivity. We propose a fundamental distinction between implicit paradigms, which quantify the statistical strength of group interactions, and explicit paradigms, which construct higher-order structural representations like hypergraphs and topological data analysis. We trace the evolution of each approach, from early Correlation-of-Correlations and information-theoretic concepts of synergy/redundancy, to the edge-centric paradigm and advanced topological methods. Through a critical analysis of conceptual, statistical, and computational challenges, we argue that the future of the field lies not in a single best method, but in a principled integration of these complementary approaches. This manuscript aims to provide a unified map and a critical perspective to guide researchers toward a robust and insightful understanding of the brain's complex, multi-level architecture.