From pairwise to higher-order brain community detection: A hypergraph signal processing approach on brain functional connectivity analysis

Abstract

Network theory is a well-established approach for characterizing brain functional networks in neuroscience. However, the brain's higher-order structures, which arise from complex, non-pairwise interactions among regions, often elude traditional graph-based approaches. While recent studies have introduced hypergraph-based methods to capture these complexities, many still depend on pairwise approximations or simplified geometric constructs such as incidence matrices, which may fail to represent authentic higher-order relationships. To address this limitation, we present a novel community detection framework for analyzing higher-order functional connectivity using real-world resting-state fMRI data. Our approach integrates multivariate information-theoretic measures with tools from hypergraph signal processing (an emerging mathematical framework tailored to model the dynamics of complex systems through higher-order interactions) enabling the identification of neurobiologically interpretable structures in the brain. Through a comparative analysis of (hyper-)graph clustering models, we uncover brain communities that remain (mostly) elusive to conventional graph-based approaches. Intriguingly, certain hypergraph modes reveal cross-network integrative patterns across distinct functional subsystems, in line with the redundancy-synergy balance that characterizes large-scale brain organization. These findings provide new insights into the architecture of higher-order functional connectivity and open promising avenues for clinical applications, particularly in studying brain disorders marked by disrupted complex connectivity patterns.

Keywords: Brain community detection; Brain functional connectivity; Hypergraph signal processing; Neuroscience; fMRI.