Deep supervised hashing methods typically learn hash functions by leveraging annotated similarities between images. Among these similarity measures, the central similarity quantization (CSQ) and its successors have excelled in optimizing the similarity between images w.r.t. their hash centers, achieving state-of-the-art performance. Nevertheless, these methods often overlook the intricate relationships and topologies inherent between different categories in generating hash centers. This limitation can impact their performance in multi-label datasets and reduce the accuracy of the generated hash codes. To address this issue, we introduce a novel deep hashing approach that incorporates label correlations using a graph convolutional network. This approach enables us to generate hash centers that effectively capture the co-occurrence correlation among diverse categories. We have conducted extensive experiments on publicly available multi-label datasets, demonstrating that our proposed method outperforms competing techniques, achieving significant performance gains.