  Existing graph clustering networks heavily rely on a predefined yet fixed
graph, which can lead to failures when the initial graph fails to accurately
capture the data topology structure of the embedding space. In order to address
this issue, we propose a novel clustering network called Embedding-Induced
Graph Refinement Clustering Network (EGRC-Net), which effectively utilizes the
learned embedding to adaptively refine the initial graph and enhance the
clustering performance. To begin, we leverage both semantic and topological
information by employing a vanilla auto-encoder and a graph convolution
network, respectively, to learn a latent feature representation. Subsequently,
we utilize the local geometric structure within the feature embedding space to
construct an adjacency matrix for the graph. This adjacency matrix is
dynamically fused with the initial one using our proposed fusion architecture.
To train the network in an unsupervised manner, we minimize the Jeffreys
divergence between multiple derived distributions. Additionally, we introduce
an improved approximate personalized propagation of neural predictions to
replace the standard graph convolution network, enabling EGRC-Net to scale
effectively. Through extensive experiments conducted on nine widely-used
benchmark datasets, we demonstrate that our proposed methods consistently
outperform several state-of-the-art approaches. Notably, EGRC-Net achieves an
improvement of more than 11.99\% in Adjusted Rand Index (ARI) over the best
baseline on the DBLP dataset. Furthermore, our scalable approach exhibits a
10.73% gain in ARI while reducing memory usage by 33.73% and decreasing running
time by 19.71%. The code for EGRC-Net will be made publicly available at
\url{https://github.com/ZhihaoPENG-CityU/EGRC-Net}.
