Autism Spectrum Disorder (ASD) is presented with significant challenges in diagnosis and intervention due to its multifaceted nature, varied symptomatology, and the high cost and time demands of behavior-based assessments. Traditional behavior-based tests, while effective, have been noted for being time-consuming and expensive. This study investigates an Electroencephalography (EEG)-based approach as a cost-effective, non-invasive alternative, utilizing minimal EEG channels to capture ASD-related abnormalities in brain oscillations with high temporal resolution. To enhance diagnostic accuracy, channel selection and feature extraction were optimized using filtering methods and particle swarm optimization. EEG data from individuals with ASD and control groups were analyzed, employing various visibility graph types and machine learning classifiers to assess coherence, causality, and time lag metrics. Results show that visibility graphs effectively capture brain connectivity differences in ASD, and machine learning classifiers trained on these features achieve higher classification accuracy compared to traditional methods. The efficacy of different visibility graph types and machine learning classifiers in ASD classification was analyzed, focusing on coherence, causality, and time lag methods. It is widely accepted that EEG signal patterns reliably reflect ASD-related abnormalities and that visibility graphs effectively represent brain connectivity. Limitations include the variability in EEG signal quality and the need for larger, more diverse datasets for validation. Comparative analysis has highlighted the pros and cons of other available methods, such as MRI and behavior-based assessments, emphasizing the superior cost-efficiency and accessibility of EEG approaches. The proposed method has been shown to outperform the existing methodologies quantitatively, achieving higher classification accuracy and performance by integrating horizontal and natural visibility graphs with machine learning classifiers. This study is presented as a significant step forward in ASD diagnosis and intervention, underscoring the potential of EEG-based technologies to revolutionize clinical practices and improve outcomes for individuals with ASD.