Introduction: The autonomic nervous system (ANS) plays a significant role in triggering and sustaining atrial fibrillation (AF) episodes. ANS activity, reflected in heart rate variability (HRV) parameters, enables comparison between sinus rhythm (SR) and pre-AF periods. However, pre-AF rhythms remain unexplored using visibility graphs (VG). Therefore, the aim of this paper is to investigate the association of natural VG (NVG) features with the AF onset prediction. Methods: The analysis was conducted on 5-minute RR interval segments of SR and pre-AF periods from the IRIDIA-AF database, incorporating classification based on standard HRV and NVG features, along with progression probability analysis. The classification analysis included different model configurations: HRV-only, NVG-only, and HRV + NVG combined features. The workflow incorporated standardization, removal of redundant features with correlation analysis, LASSO based feature selection, and classification using Gaussian Naive Bayes. Results: The results showed statistically significant improvement of area under the receiver operating characteristics curve (AUROC) for combined feature sets (AUROC = 0.74 [95% CI:0.55,0.81]) to single feature sets (HRV-only - AUROC = 0.58 [95% CI:0.45,0.71]; NVG-only - AUROC = 0.55 [95% CI:0.45,0.65]) on the separate test set (49 SR and 37 pre-AF segments). Shapley values were computed to interpret the model, indicating that standard HRV features have greater importance compared to NVG features. The probability progression analysis in the pre-AF period demonstrates the increase of probability approaching the AF onset however shows no visual difference between male and female patients. These findings suggest that integrating NVG analysis with standard HRV parameters provides deeper insight into heart rate dynamics during the pre-AF period.