Arrhythmias, detectable through electrocardiograms (ECGs), pose significant health risks, underscoring the need for accurate and efficient automated detection techniques. While recent advancements in graph-based methods have demonstrated potential to enhance arrhythmia classification, the challenge lies in effectively representing ECG signals as graphs. This study investigates the use of Visibility Graph (VG) and Vector Visibility Graph (VVG) representations combined with Graph Convolutional Networks (GCNs) for arrhythmia classification under the ANSI/AAMI standard, ensuring reproducibility and fair comparison with other techniques. Through extensive experiments on the MIT-BIH dataset, we evaluate various GCN architectures and preprocessing parameters. Our findings demonstrate that VG and VVG mappings enable GCNs to classify arrhythmias directly from raw ECG signals, without the need for preprocessing or noise removal. Notably, VG offers superior computational efficiency, while VVG delivers enhanced classification performance by leveraging additional lead features. The proposed approach outperforms baseline methods in several metrics, although challenges persist in classifying the supraventricular ectopic beat (S) class, particularly under the inter-patient paradigm.