Graph-based hashing has recently emerged as a prominent research area due to the rapid expansion of multimodal datasets. Most existing graph-based methods rely on Graph Convolutional Networks (GCNs) as a guiding mechanism, primarily because of the unique characteristics of cross-modal retrieval tasks. However, these methods often encounter several challenges: 1) They struggle to preserve the inherent similarities within the original datasets. 2) They frequently employ intractable binary quadratic programs, which limits their scalability when dealing with extensive data volumes. In this paper, we introduce an innovative framework termed Adversarial Graph Convolutional Network Hashing (AGCNH), which leverages dual-cycle Generative Adversarial Networks (GANs) alongside GCNs. This framework incorporates two asymmetric graph layers and a standard graph layer, effectively addressing the issue of excessive parameterization in GCNs and enabling the direct generation of binary codes. To demonstrate the effectiveness of our proposed method, we have conducted experiments on four widely used datasets, thereby validating the robustness and applicability of our approach.