The wide spread of rumors on social media has caused a negative impact on people's daily life, leading to potential panic, fear, and mental health problems for the public. How to debunk rumors as early as possible remains a challenging problem. Existing studies mainly leverage information propagation structure to detect rumors, while very few works focus on correlation among users that they may coordinate to spread rumors in order to gain large popularity. In this paper, we propose a new detection model, that jointly learns both the representations of user correlation and information propagation to detect rumors on social media. Specifically, we leverage graph neural networks to learn the representations of user correlation from a bipartite graph that describes the correlations between users and source tweets, and the representations of information propagation with a tree structure. Then we combine the learned representations from these two modules to classify the rumors. Since malicious users intend to subvert our model after deployment, we further develop a greedy attack scheme to analyze the cost of three adversarial attacks: graph attack, comment attack, and joint attack. Evaluation results on two public datasets illustrate that the proposed MODEL outperforms the state-of-the-art rumor detection models. We also demonstrate our method performs well for early rumor detection. Moreover, the proposed detection method is more robust to adversarial attacks compared to the best existing method. Importantly, we show that it requires a high cost for attackers to subvert user correlation pattern, demonstrating the importance of considering user correlation for rumor detection.