Video-based gait analysis can be defined as the task of diagnosing pathologies, such as ataxia, using videos of patients walking in front of a camera. This paper presents a graph convolution network called AtGCN for detecting ataxic gait and identifying its severity using 2D videos. The problem is especially challenging as the deviation of an ataxic gait from a healthy gait is very subtle. The datasets for ataxic gait detection are also quite small, with the largest dataset having only 149 videos. The paper addresses the first problem using special spatiotemporal graph convolution that successfully captures important gait-related features. To handle the small dataset size, a deep spatiotemporal graph convolution network pre-trained on an action recognition dataset is systematically truncated and then fine-tuned on the ataxia dataset to obtain the AtGCN model. The paper also presents an augmentation strategy that segments a video sequence into multiple gait cycles. The proposed AtGCN model then operates on a graph of body part locations belonging to a single gait cycle. The evaluation results support the strength of the proposed AtGCN model, as it outperforms the state-of-the-art in detection and severity prediction with an accuracy of 93.46% and a MAE of 0.4169, respectively, while being 5.5 times smaller than the state-of-the-art.