## 4 Results
### Graph Theoretical Analysis  
Global efficiency:  
Global efficiency is a measure used in graph theory-based brain-network analyses and indicates how efficiently information is exchanged over the network. The scatter plots presented in Figure 7 illustrate a comparative study of global efficiency across four frequency bands--theta, alpha, beta, and gamma--between subjects categorized based on their performance in a cognitive task. The scatter plot for good-performance subjects on the left exhibits global efficiency values predominantly ranging from approximately 0.3 to 0.8, with the gamma band showing a particularly tight clustering around the 0.6 to 0.8 range. Figure 6: Topomap and corresponding connectivity graph of good- vs. bad-performance subjects in four frequency bands. (**a**) Topomaps of good- vs. bad-performance subjects at the onset of the task (6.4 s). (**b**) Connectivity maps of corresponding frequency bands of good- vs. bad-performance subjects at 6.4 s.  
This suggests a robust association between high global efficiency in the gamma frequency and enhanced cognitive processing. Conversely, the scatter plot for bad-performance subjects on the right demonstrates a broader spread of values, mainly between 0.2 and 0.7, with none reaching the efficiency peaks observed in the good-performance group. The comparative dearth of higher efficiency values in the bad performers highlights a potential correlation between lower global efficiency and suboptimal cognitive task execution. These visual data insights thus offer a quantifiable link between the efficiency of neural connectivity and cognitive performance levels, potentially guiding future interventions aimed at cognitive enhancement. Clustering coefficient:  
The clustering coefficient, a quantitative network connectivity metric, gauges the extent to which nodes within a graph--here representing EEG channels--tend to cluster. The bar chart (Figure 8) depicts the clustering coefficients across EEG channels, delineating the contrast between subjects with good and bad performance on a cognitive task. As illustrated, the good-performance group exhibits notably higher clustering coefficients across a range of EEG channels, with the most pronounced differences observed at channels Fp1 (\(\sim\)0.005 for bad vs. \(\sim\)0.035 for good), F8 (\(\sim\)0.007 for bad vs. \(\sim\)0.045 for good), T5 (\(\sim\)0.007 for bad vs. \(\sim\)0.04 for good), and O1 (\(\sim\)0.005 for bad vs. \(\sim\)0.035 for good). Conversely, channels such as Fp2, F3, and Fz show a less marked contrast, though the good-performance group still maintains a lead. The coefficient disparity implies a more robust local connectivity within the brain's neural network among the high-performing subjects, potentially facilitating more effective cognitive processing. This relationship is especially evident in the frontal and occipital regions--known for their roles in higher-order cognitive functions and visual processing, respectively--where higher coefficients correlate with better task performance. Conversely, the lower clustering coefficients observed in the bad-performance group across channels such as Fp2 (\(\sim\)0.005), F3 (\(\sim\)0.01), and Fz (\(\sim\)0.015) suggest a less interconnected network, which might contribute to their suboptimal cognitive task outcomes. These insights emphasize the significance of localized brain network configurations in cognitive abilities and task execution. Betweenness centrality:  
Betweenness centrality is a measure from graph theory that calculates how often a node serves as a connecting point on the shortest route between two other nodes. In the context of neural networks, it reflects the importance of a particular region in the flow of information throughout the brain. The bar graph (Figure 9) depicts the mean betweenness  
Figure 7: Global efficiency of BSL functional-connectivity graphs for good (**left**) vs. bad (**right**) performance subjects in theta, alpha, beta, and gamma frequency bands.