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Network alignment is a critical steppingstone behind a variety of multi-network mining tasks. Most of the existing methods essentially optimize a Frobenius-like distance or ranking-based loss, ignoring the underlying geometry of graph data. Optimal transport (OT), together with Wasserstein distance, has emerged to be a powerful approach accounting for the underlying geometry explicitly. Promising as it might be, the state-of-the-art OT-based alignment methods suffer from two fundamental limitations, including (1) effectiveness due to the insufficient use of topology and consistency information and (2) scalability due to the non-convex formulation and repeated computationally costly loss calculation. In this paper, we propose a position-aware regularized optimal transport framework for network alignment named PARROT. To tackle the effectiveness issue, the proposed PARROT captures topology information by …