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Estimating causal effects from observational data has garnered significant attention in recent years, as it facilitates decision-making in various domains, such as healthcare, economy, and social science. Recently, many studies have focused on networked observational data, utilizing the auxiliary network structure to infer hidden confounders for improved performance in causal effect estimation. However, networked observational data often contains noise in practical scenarios and existing methods often experience a severe performance decline when the edge noise is present in terms of the graph structure, leading to disrupted and biased causal estimation. Thus, denoising the collected graph and getting the optimal network structure is critical for precise causal effect estimation. In this paper, we propose a novel approach, referred as EDge reweIghTing Of multi-subgRaph (EDITOR), to eliminate the graph noise for robust causal effect estimation. Specifically, by utilizing graph neural network, EDITOR partitions the perturbed graph into distinct subgraphs based on the edge type and learning their importance weights for each subgraph. By doing so, our method effectively uncovers the clean graph structure from perturbed networked data while preserving the underlying causal information. Extensive experiments are conducted over different datasets and perturbations, demonstrating that the proposed methods achieve significantly higher performance and robustness than state-of-the-art causal effect estimation methods.