# Hypergraph Analysis of Functional Brain Connectivity During Figurative Attention
###### Abstract  
Hypergraph analysis extends traditional graph theory by enabling the study of complex, many-to-many relationships in networks, offering powerful tools for understanding brain connectivity. This case study introduces a novel methodology for constructing both graphs and hypergraphs of functional brain connectivity during figurative attention tasks, where subjects interpret the ambiguous Necker cube illusion. Using a frequency-tagging approach, we simultaneously modulated two cube faces at distinct frequencies while recording electroencephalography (EEG) responses. Brain connectivity networks were constructed using multiple measures--coherence, cross-correlation, and mutual information--providing complementary insights into functional relationships between regions. Our hypergraph analysis revealed distinct connectivity patterns associated with attending to different cube orientations, including previously unobserved higher-order relationships between brain regions. The results demonstrate bilateral cortico-cortical interactions and suggest integrated processing hubs that may coordinate visual attention networks. This methodological framework not only advances our understanding of the neural basis of visual attention but also offers potential applications in attention monitoring and clinical assessment of attention disorders. While based on a single subject, this proof-of-concept study establishes a foundation for larger-scale investigations of brain network dynamics during ambiguous visual processing. hypergraph; brain connectivity; cognitive neuroscience; visual perception; electroencephalography (EEG); coherence; cross-correlation; mutual information; neuronal networks +
Footnote †: journal: Applied sciences  
0000-0001-5000-0000-0000-0000-0000-0000-0000-0000-0000-00000-0000-00000-0000-0  
theory [2; 3]. By representing brain regions as nodes and their interactions as links, this approach has facilitated the study of biohythmic connections across different brain areas [4; 5]. It has also proven valuable in identifying individual cognitive differences [6], diagnosing neurological disorders [7; 8; 9], and assessing aging-related neural changes [10; 11; 12; 13]. EEG-based functional connectivity networks have become essential tools for understanding individual variability in brain activation patterns during cognitive tasks [14; 15]. These networks provide valuable insights into how different brain regions interact, shedding light on the neural mechanisms underlying attention and other cognitive processes. Traditional graph-theoretic approaches model functional connectivity by representing brain regions as vertices and their functional interactions as edges [4]. However, these methods primarily capture second-order relationships--interactions between pairs of brain regions--while neglecting higher-order relationships that are fundamental to complex neural processing. Since cognitive processes such as attention involve dynamic and multifaceted interactions across multiple brain regions, conventional functional connectivity networks fail to provide a complete picture by only capturing pairwise relationships. To overcome this limitation, hypergraph-based connectivity models have been introduced. Unlike traditional graphs, hypergraphs allow for the representation of multi-node interactions through hyperedges, enabling a richer and more comprehensive characterization of brain connectivity. Hypergraphs have recently gained prominence as an advanced framework for investigating brain connectivity [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. Unlike conventional graphs that are limited to pairwise relationships, hypergraphs extend graph theory to model complex, multi-region interactions simultaneously [31; 32]. This approach offers a more nuanced and holistic view of functional brain networks by capturing the intricate, dynamic interactions among multiple neural regions.