# Initialize GroupKFold for cross-validation group_kfold = GroupKFold(n_splits = 5)
## 5 Results
### Synthetic Data Analysis  
The synthetic data analysis provided a more robust foundation for understanding information diffusion. With 100 networks and 3600 observations, we achieved substantially higher model performance and more reliable feature importance rankings. The performance comparison revealed that Tree-based models performed significantly better than linear models (Figure 23). Gradient Boosting achieved the highest performance (R\({}^{2}\) = 0.847 \(\pm\) 0.032), followed closely by Random Forest (R\({}^{2}\) = 0.845 \(\pm\) 0.032). SVR showed moderate performance (R\({}^{2}\) = 0.743), while linear models performed relatively poorly. The feature importance analysis (Figure 24) revealed that peak_speed_time was the dominant feature (importance = 0.848), followed by avg_degree (importance = 0.101). Other features played much smaller roles, suggesting that temporal dynamics and average connectivity were the most critical factors affecting information diffusion. We also conducted comprehensive residual analysis to validate model assumptions and identify potential issues (Figures 25-28). The residual analysis showed well-behaved errors with no systematic patterns, although the Shapiro-Wilk test indicated non-normally distributed residuals (W = 0.841, \(p<\,0.001\)). This suggested some complexity in the model that was not fully captured by a normal error distribution. In contrast to the real data analysis, peak_speed_time emerged as the overwhelmingly dominant feature (importance = 0.848), with avg_degree as a distant second (importance =  
Figure 23: Model performance comparison on synthetic data. Green bars indicate high-performing models (R\({}^{2}\) > 0.7), orange bars show moderate performance, and purple bars represent all models’ Mean Absolute Error values (lower is better). 0.101). This suggests that temporal dynamics of information spread may be more important than static network properties. The remaining features showed minimal individual importance (<0.01). Figure 24: Feature importance analysis. Figure 25: Actual vs Predicted Coverage (Gradient Boosting). Purple circles represent individual data points, red dashed line shows perfect prediction (y=x), and green line shows the fitted regression line with equation y = 0.863x + 0.055 (R\({}^{2}\) = 0.871). When evaluated on the entire dataset, the final Gradient Boosting model achieved an R\({}^{2}\) of 0.871, demonstrating strong predictive power. However, the residuals were not normally distributed (Shapiro-Wilk W = 0.841, \(p<~{}0.001\)), suggesting some complexity in the data which was not fully captured by the model. Analysis of the diffusion patterns (Figure 29) revealed that Random networks achieved the highest average coverage (0.653), followed by Small-World networks (0.505). Tree networks showed the lowest coverage (0.219), likely due to their limited connectivity. The effect of graph type was statistically significant (F = 346.325, \(p<~{}0.001\)). Figure 27: Residual distribution. Purple bars show the histogram of residual values, red curve represents the fitted normal distribution overlay, and red dashed line indicates the mean of residuals (zero). Figure 26: Residual plot. Purple circles show residual values for each prediction, red dashed line indicates zero residuals (perfect prediction), and green line shows the residual trend. Mean residuals = 0.000, Standard deviation = 0.143. Interestingly, delay type (Figures 29 and 30) showed no significant effect on coverage across synthetic networks (F = 0.072, \(p\) = 0.930). This suggests that simpler constant delay models may be adequate for many applications, allowing practitioners to focus resources on optimizing network structure and transmission probability rather than precise delay distributions. Figure 28: Q-Q plot of residuals. Blue dots represent actual residual quantiles plotted against theoretical normal quantiles, red line shows the expected relationship for perfect normal distribution. Deviations from the red line indicate departures from normality.