# Hypergraph Analysis of Functional Brain Connectivity During Figurative Attention
## 5 Graph Construction
### Connectivity Graphs Based on Coherence  
To construct connectivity graphs, we first calculate coherence between signals from each pair of electrodes for the MI, MLV, and MRV tests in the \(f_{1}\) and \(f_{2}\) spectral regions  
Figure 4: Wavelets from channel O1, illustrating the spectral energy associated with figurative attention directed towards (**a**) left-cube (MLV) and (**b**) right-cube (MRV) orientations. The peak wavelet energy is observed within distinct frequency regions: (**a**) \(f_{1}\) when the subject perceives the cube as left-oriented, and (**b**) \(f_{2}\) when the subject perceives the cube as right-oriented. The frequency ranges \(f_{1}\) and \(f_{2}\) are demarcated by horizontal dashed lines, highlighting the specific bands where attentional focus is most pronounced. using Equation (9). Next, we computed the differences \(\Delta Coh_{L}\) and \(\Delta Coh_{R}\) associated with attention using Equation (14). The resulting labeled graphs of coherence (\(\Delta Coh>0\)) and anticoherence (\(\Delta Coh<0\)) are displayed in Figures 5 and 6, respectively. The corresponding \(16\times 16\) coherence matrices are provided in Figures 12 and 13 in Appendix B. The colors in Figures 5 and 6 represent the numerical weights of the links, illustrating coherence differences (\(\Delta Coh\)) resulting from shifts in attention. The strongest links are emphasized with bold lines and labeled with their corresponding coherence differences. We also calculated the total sum of link weights for each node, displaying these values next to the nodes with the highest sums, which are marked with orange dots. In contrast, nodes with the lowest (negative) labels are indicated with violet dots. A significant contrast in coherence patterns emerges between frequency regions \(f_{1}\) and \(f_{2}\). When attention is directed toward the left-cube orientation, coherence increases prominently between the left anterior frontal (F7) and midline parietal (Pz) and left parietal (P3) lobes at \(f_{1}\) (upper left panel, Figure 5). In contrast, at \(f_{2}\), coherence increases symmetrically in the right hemisphere, particularly between the right anterior frontal (F8), midline parietal (Pz), and right parietal (P4) lobes (lower left panel, Figure 5). These findings suggest that the anterior frontal lobes play a crucial role in figurative attention. For right-cube attention, coherence increases between the left parietal (P3) and midline central (Cz) lobes, as well as between the midline parietal (Pz) and midline central (Fz) lobes at \(f_{1}\) (upper right panel, Figure 5). However, at \(f_{2}\), coherence significantly increases between the occipital cortex (O1, Oz, O2) and the left prefrontal lobe (FP1) (lower right panel, Figure 5). The left parietal lobe (FP2) (lower right panel, Figure 5) is the right lobe (FP2) (lower right panel, Figure 5). The right lobe (FP2) (lower right panel, Figure 5) is the right lobe (FP2) (lower right panel, Figure 5). panel, Figure 5). These observations suggest that the left prefrontal cortex may play a key role in processing right-cube orientation, as the frequency \(f_{2}\) is applied to the right face of the cube. Our findings align with prior studies, such as [PERSON] and [PERSON] (2017), which also reported attention-related activity in the prefrontal and parietal cortices. A critical aspect of these results is the simultaneous decrease in coherence between certain brain regions, indicating that attention not only strengthens specific neural connections but also selectively disconnects others. Given the brain's energy-intensive nature, this redistribution likely reflects an optimization of cognitive resources. Figure 6 visualizes this selective disconnectivity through anticoherence graphs. The results reveal a notable reduction in coherence at \(f_{1}\) between the midline central (Cz) and left frontal (F3) lobes, as well as between the midline central (Cz) and left prefrontal (FP1) lobes during left-cube attention (upper left panel, Figure 6).