## 1 Introduction  
Understanding the intricacies of brain connectivity in response to diverse stimuli is crucial for unraveling the mechanisms underlying information processing and decision making within the brain. This study delves into three essential forms of brain connectivity: structural, functional, and efficient [1, 2, 3, 4]. Structural connectivity entails the identification of anatomical neural networks, revealing potential pathways for neural communication [5, 6]. On the other hand, functional connectivity explores active brain regions exhibiting correlated frequency, phase, and/or amplitude [7]. Finally, effective connectivity utilizes information from functional connectivity to discern the dynamic flow of information within the brain [8, 9]. Measurement of effective and functional connectivity can be conducted in both the frequency domain, employing methods such as coherence [10], and in the time domain, utilizing approaches like Granger causality [4] or artificial-neural-network-based functional connectivity [11]. When a sufficiently large population of neurons synchronizes, their electrical and magnetic activities become detectable outside the skull through techniques like electroencephalography (EEG) and magnetoencephalography (MEG) [12]. While EEG measures return or bulk currents outside the neuron (secondary currents), MEGcaptures ionic currents inside the neuron (primary currents). Notably, MEG holds a distinct advantage over EEG due to its superior spatial resolution, rendering it an exceptional tool for investigating and characterizing interactions between distinct brain regions [13]. To study functional connectivity, some researchers use approaches borrowed from graph theory [14]. Using connections between the biorhythms of the brain in its various parts, a model of a complex network is recreated, in which parts of the brain are considered as nodes, and the connection forces between them are considered as links [15; 16]. Using this approach makes it possible to identify not only individual cognitive differences between subjects [17], but also helps to diagnose some diseases at an early stage [18; 19; 20] and also monitor the aging process [21; 22; 23; 24]. One of the important measures that can be used to quantify neuronal synchrony is event-related coherence [10; 25; 26]. It examines the frequency domain relationship between two signals, indicating the degree to which their spectral components are synchronized. Essentially, it is an assessment of the constancy of the relative amplitude and phase between two signals within a given frequency range. There is a linear mathematical method that creates a symmetrical matrix, devoid of any directional information. Identical signals produce a coherence value of 1, while the coherence value approaches 0 as the difference between the signals in question increases. Since then, coherence has been used in many brain connectivity studies with both patients and control individuals; these include but are not limited to studies of working memory [27], brain lesions [28], hemiparesis [29], resting state networks [30], schizophrenia [31; 32], favorable responses to panic medications [33], and motor imagery [34]. As a result of the unique characteristics of human brains, distinct patterns of coherent neuronal activity were observed among different subjects. For instance, the presentation of flickering visual stimuli induces coherent responses in the visual cortex of subjects at both the flicker frequency and its harmonics, resulting in varied sizes of coherent neural networks [35; 36]. In this work, we employ hypergraph analysis, a technique rooted in dynamic graph theory [37], to investigate functional connectivity. We analyze variations in functional connectivity networks using MEG data collected during the observation of flickering images. This approach is an extension of conventional graph theory methods. Specifically, we begin by defining a standard functional network that connects nodes across consecutive time segments.