# Hypergraph Analysis of Functional Brain Connectivity During Figurative Attention
###### Abstract
Through hypergraph analysis, researchers can gain deeper insights into how brain regions integrate, synchronize, and adapt to support cognitive functions, providing novel perspectives on neural organization and functionality. Hypergraphs representing brain connectivity have been constructed using neurophysiological data from various imaging modalities. Most studies have focused on functional magnetic resonance imaging (fMRI) data, particularly in the resting state [16; 17; 18; 19; 20; 21; 22; 23; 24]. Structural MRI has also been employed for hypergraph-based connectivity modeling [25]. Additionally, researchers have developed hypergraphs using multimodal data that integrate MRI with fluorodeoxyglucose positron emission tomography (PET) and cerebrospinal fluid analysis [29]. Beyond MRI-based studies, both invasive intracranial EEG [26] and noninvasive EEG [27; 28] have been used to construct hypergraphs. Magnetoencephalography (MEG) data have also been explored in hypergraph-based connectivity studies [30]. The versatility of hypergraph-based connectivity modeling has led to applications in diverse areas, including emotion recognition [22; 27], motor imagery [28], and the diagnosis of neurological disorders such as mild cognitive impairment [18; 21; 29], schizophrenia [20], autism spectrum disorder [24], Alzheimer's disease [25; 29], and epileptic seizure detection [26]. Many of these studies employ correlation-based metrics to measure functional connectivity, with Pearson correlation being a widely used approach for quantifying neural interactions [33]. Given the importance of attentional processes in cognitive health, hypergraph-based connectivity models offer a promising avenue for understanding the neural mechanisms underlying attention and related cognitive functions. Attention is a crucial cognitive function, and its impairment is associated with various neurological and psychiatric disorders, including cognitive decline, dementia, attention deficit hyperactivity disorder, and autism spectrum disorder. These conditions affect a broad range of cognitive and behavioral abilities, such as learning, problem-solving, communication, and social interaction. Individuals with attention deficits may struggle to express their experiences or understand others' perspectives, which can hinder their development of essential social and learning skills. Electroencephalography (EEG) is a widely used modality for assessing attention. While many studies have focused on the relationship between P-300 event-related potentials and attention in EEG signals, others have explored spectral analysis as an alternative approach [34; 35; 36; 37; 38]. The use of hypergraphs to model brain connectivity could provide deeper insights into the neural mechanisms underlying attention deficits by capturing the complex, multi-dimensional relationships within brain networks. This approach may complement traditional EEG-based methods, offering a more comprehensive understanding of attention-related impairments and their neural correlates. This study is motivated by the growing interest in machine learning techniques for the early diagnosis and prediction of neurodegenerative diseases based on hypergraphs of brain connectivity. The primary objective of this study is to develop a method for constructing hypergraphs of brain connectivity to enhance our understanding of brain functionality during figurative attention. Unlike traditional pairwise graphs, hypergraphs provide a more comprehensive representation by capturing the most significant connections and disconnections across multiple brain lobes, identified through different connectivity measures such as coherence, correlation, and mutual information. To investigate this, we use the Necker cube--an ambiguous figure requiring attentional focus for orientation interpretation (left- or right-facing).