With the continuous development of speech recognition technology, speaker verification (SV) has become an important method for identity authentication. Traditional SV methods rely on handcrafted feature extraction, while deep learning has significantly improved system performance. However, the scarcity of labeled data still limits the widespread application of deep learning in SV. Self-supervised learning, by mining latent information in large unlabeled datasets, enhances model generalization and is a key technology to address this issue. DINO is an efficient self-supervised learning method that generates pseudo-labels from unlabeled speech data through clustering, supporting subsequent training. However, clustering may produce noisy pseudo-labels, which can reduce overall recognition performance. To address this issue, this paper proposes an improved clustering framework based on similarity connection graphs and Graph Convolutional Networks. By leveraging GCNs' ability to model structured data and incorporating relational information between nodes in the similarity connection graph, the clustering process is optimized, improving pseudo-label accuracy and enhancing the robustness and performance of the self-supervised speaker verification system. Experimental results show that this method significantly improves system performance and provides a new approach for self-supervised speaker verification. Index Terms: Speaker Verification, Self-Supervised Learning, DINO, Clustering Algorithm, Graph Convolutional Network, Similarity Connection Graph