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   Abstract Recent years have witnessed a rocketing growth of machine learning methods on graph data, especially those powered by effective neural networks. Despite their success in different real‐world scenarios, the majority of these methods on graphs only focus on predictive or descriptive tasks, but lack consideration of causality. Causal inference can reveal the causality inside data, promote human understanding of the learning process and model prediction, and serve as a significant component of artificial intelligence (AI). An important problem in causal inference is causal effect estimation, which aims to estimate the causal effects of a certain treatment (e.g., prescription of medicine) on an outcome (e.g., cure of disease) at an individual level (e.g., each patient) or a population level (e.g., a group of patients). In this paper, we introduce the background of causal effect estimation from observational data, envision the challenges of causal effect estimation with graphs, and then summarize representative approaches of causal effect estimation with graphs in recent years. Furthermore, we provide some insights for future research directions in related area. Link to video abstract:https://youtu.be/BpDPOOqw‐ns 

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