Recent studies indicate that variations in the expression of circular RNA (circRNA) can alter cellular drug sensitivity, which in turn significantly impacts drug efficacy and plays a crucial role in human health and disease treatment. Thus, predicting the associations between circRNA and drug sensitivity is essential. In this study, to enhance the prediction accuracy, we introduce a novel method named MHCDA that leverages graph convolutional networks and hypergraph convolutional networks to extract both local and global information of the circRNA-drug network. Specifically, MHCDA first constructs homogeneous graphs for circRNAs and drugs through similarity fusion networks, then obtain the representations of circRNAs and drugs using graph convolutional networks. On the other hand, we utilize hypergraph convolutional networks to extract more complex higher-order interactions between drugs and circRNAs, respectively. Utilizing Contrastive Learning to Analyze circRNA Feature Representations and Pharmacological Feature Representations Across Various Convolutional Architectures. Meanwhile, we utilize autoencoders to extract circRNA and drug features from the established associations between circRNAs and drugs. Finally, we integrate the various features obtained to predict the relationship between circRNA and drug sensitivity. Experiments reveal that the AUC and AUPR values of MHCDA are 0.918 and 0.929, respectively, surpassing those of other advanced models.