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Online forums that allow participatory engagement between users have been transformative for public discussion of important issues. However, debates on such forums can sometimes escalate into full blown exchanges of hate or misinformation. An important tool in understanding and tackling such problems is to be able to infer the argumentative relation of whether a reply is supporting or attacking the post it is replying to. This so called polarity prediction task is difficult because replies may be based on external context beyond a post and the reply whose polarity is being predicted. We propose GraphNLI, a novel graph-based deep learning architecture that uses graph walk techniques to capture the wider context of a discussion thread in a principled fashion. Specifically, we propose methods to perform root-seeking graph walks that start from a post and captures its surrounding context to generate additional embeddings for the post. We then use these embeddings to predict the polarity relation between a reply and the post it is replying to. We evaluate the performance of our models on a curated debate dataset from Kialo, an online debating platform. Our model outperforms relevant baselines, including S-BERT, with an overall accuracy of 83%.