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Graphs (i.e., networks) are ubiquitous in daily life, as they can effectively model a plethora of real-world systems with connected units, such as social networks and biological networks. Recent years have witnessed rapid development in graph-based machine learning (GML) in various high-impact domains. Currently, the mainstream GML methods are based on statistical learning, e.g., utilizing the statistical correlations between node features, graph structure, and labels for node classification. However, statistical learning has been widely criticized for only capturing the superficial relations between variables in the data system, and consequently, rendering the lack of trustworthiness in real-world applications. Therefore, it is crucial to understand the causality in the data system and the learning process. Causal inference is the discipline that investigates the causality inside a system, for example, to identify and estimate the causal effect of a certain treatment (e.g., wearing a face mask) on an important outcome (e.g., COVID-19 infection). Involving the concepts and philosophy of causal inference in ML methods is often considered significant for human-level intelligence and can serve as the foundation of artificial intelligence (AI). However, most traditional causal inference studies rely on strong assumptions, and focus on independent and identically distributed (i.i.d.) data, while causal inference on graphs is faced with many barriers. Therefore, we aim to bridge the gap between causal inference and GML.