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Domain adaptation techniques, which focus on adapting models between distributionally different domains, are rarely explored in the video recognition area due to the significant spatial and temporal shifts across the source (i.e. training) and target (i.e. test) domains. As such, recent works on visual domain adaptation which leverage adversarial learning to unify the source and target video representations and strengthen the feature transferability are not highly effective on the videos. To overcome this limitation, in this paper, we learn a domain-agnostic video classifier instead of learning domain-invariant representations, and propose an Adversarial Bipartite Graph (ABG) learning framework which directly models the source-target interactions with a network topology of the bipartite graph. Specifically, the source and target frames are sampled as heterogeneous vertexes while the edges connecting two types of nodes measure the affinity among them. Through message-passing, each vertex aggregates the features from its heterogeneous neighbors, forcing the features coming from the same class to be mixed evenly. Explicitly exposing the video classifier to such cross-domain representations at the training and test stages makes our model less biased to the labeled source data, which in-turn results in achieving a better generalization on the target domain. To further enhance the model capacity and testify the robustness of the proposed architecture on difficult transfer tasks, we extend our model to work in a semi-supervised setting using an additional video-level bipartite graph. Extensive experiments conducted on four benchmarks evidence the effectiveness of the proposed approach over the SOTA methods on the task of video recognition.