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Deep graph clustering (DGC) has been a promising method for clustering graph data in recent years. However, existing research primarily focuses on optimizing clustering outcomes by improving the quality of embedded representations, resulting in slow-speed complex models. Additionally, these methods do not consider changes in node similarity and corresponding adjustments in the original structure during the iterative optimization process after updating node embeddings, which easily falls into the representation collapse issue. We introduce an Efficient Graph Auto-Encoder (EGAE) and a dynamic graph weight updating strategy to address these issues, forming the basis for our proposed Fast DGC (FastDGC) network. Specifically, we significantly reduce feature dimensions using a linear transformation that preserves the original node similarity. We then employ a single-layer graph convolutional filtering approximation to replace multiple layers of graph convolutional neural network, reducing computational complexity and parameter count. During iteration, we calculate the similarity between nodes using the linearly transformed features and periodically update the original graph structure to reduce edges with low similarity, thereby enhancing the learning of discriminative and cohesive representations. Theoretical analysis confirms that EGAE has lower computational complexity. Extensive experiments on standard datasets demonstrate that our proposed method improves clustering performance and achieves a speedup of 2–3 orders of magnitude compared to state-of-the-art methods, showcasing outstanding performance. The code for our model is available at https://github.com/Marigoldwu/FastDGC. Furthermore, we have organized a portion of the DGC code into a unified framework, available at https://github.com/Marigoldwu/A-Unified-Framework-for-Deep-Attribute-Graph-Clustering. [ABSTRACT FROM AUTHOR]