###### Abstract  
Analyzing brain activity during mental arithmetic tasks provides insight into psychological disorders such as ADHD, dyscalculia, and autism. While most research is conducted on the static functional connectivity of the brain while performing a cognitive task, the dynamic changes of the brain, which provide meaningful information for diagnosing individual differences in cognitive tasks, are often ignored. This paper aims to classify electroencephalogram (EEG) signals for rest vs. mental arithmetic task performance, using Bayesian functional connectivity features in the sensor space as inputs into a graph convolutional network. The subject-specific (intrasubject) classification performed on 36 subjects for rest vs. mental arithmetic task performance achieved the highest subject-specific classification accuracy of 98% and an average accuracy of 91% in the beta frequency band, outperforming state-of-the-art methods. In addition, statistical analysis confirms the consistency of Bayesian functional connectivity features compared to traditional functional connectivity features. Furthermore, the graph-theoretical analysis of functional connectivity networks reveals that good-performance subjects had higher global efficiency, betweenness centrality, and closeness centrality than bad-performance subjects. The ablation study on the classification of three cognitive states (subtraction, music, and memory) achieved a classification accuracy of 97%, and visual working memory (n-back task) achieved a classification accuracy of 94%, confirming the consistency and reliability of the proposed methodology. EEG; functional connectivity; Bayesian functional connectivity; graph convolutional network +
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modalities. Effective connectivity determines the causal interactions (direct or indirect) of the brain regions [10]. This paper focuses on functional-connectivity estimation and classification, which helps to identify the underlying brain activity while performing a cognitive task. The statistical functional-connectivity estimation methods proposed in the literature infer amplitude [11], spectral [12], and phase [13] correlations, focusing mainly on estimating the correlations on pairwise signals (such as Pearson's correlation). These methods impose correlations between the regions of interest (ROIs) representing edge strengths between the nodes. Therefore, these methods capture only the secondary correlation between network nodes, and many confounding interactions are imposed, often thresholded by an arbitrary threshold. Researchers have used partial correlation that provides binary results of the existing correlation to avoid spurious connections between the nodes. Other sparse representation methods [14], such as the graphical least absolute shrinkage and selection operator (LASSO), use an inverse covariance matrix to impose correlations between the nodes. However, all these methods assume that the connectivity patterns are static, ignoring the dynamic behavior of brain functional connectivity. Some recent approaches have focused on dynamic functional connectivity over time [15]. These approaches have tried to estimate the covariance matrices of small time intervals from the fMRI data [16]. Later, these covariance matrices are clustered to form a tensor of connectivity matrices and fed to a classification model [17]. These methods are primarily developed on the fMRI data, where the functional-connectivity estimation of other neuroimaging and neurophysiological methods are unexplored. Researchers discovered that EEG is suitable for capturing the dynamicity of brain responses generated by synaptic transitions of millions of neurons in different frequency and time domains [18; 19; 20]. In addition, with its higher temporal resolution than fMRI, an EEG can directly acquire dynamic postsynaptic activity in the cerebral cortex. Hence, an EEG helps assess the synchronous fluctuations of the brain while performing a cognitive task [21].