# A Scalable Deep Network for Graph Clustering
## 1 Introduction  
Graph-structured data often contains abundant node features and topological information. Benefiting from its powerful expressive ability, graph-structured data are often used to model drug discovery [1], social networks [2], and recommender systems [3]. Moreover, the graph clustering task has attracted extensive attention as an important part of unsupervised learning on graphs. There are many directions in graph clustering tasks, such as node-wise graph clustering, and graph-wise graph clustering. In recent years, Graph Neural Networks (GNNs) have become a popular field in deep learning, which improves the performance of graph clustering tasks effectively. Graph Convolutional Networks (GCNs) [4] are one of the representative methods that can utilize node features and topology information to obtain low-dimensional embeddings. On this basis, many graph clustering models combined with deep learning techniques have been proposed to achieve state-of-the-art effects. [PERSON] et al. [5] learn embedding through GCN layers, then the decoder reconstructs the features as similar as possible to the original features. [PERSON] et al. [6] optimize the aforementioned model to solve the norm-zero tendency of isolated nodes. In addition, [PERSON] et al. [7] combine graph convolution with the adversarialtraining method. However, the above models fail to pay attention to the importance of nodes. Therefore, [PERSON] et al. [8] introduce the attention mechanism into the graph convolution, which can aggregate the information based on nodes' importance. [PERSON] et al. [9] adopt the receptive field with an attention mechanism to encode the features and jointly optimize the clustering and embedding module. Although the models with the graph auto-encoder as the backbone network can generate the embeddings effectively; it ignores the information in the data structure. Combining different orders of the embeddings and the structural information, [PERSON] et al. [10] integrate structural information into a deep clustering method for the first time to improve the clustering effect. In addition, [PERSON] et al. [11] adopts the combination of deep clustering and the graph auto-encoder to design a triple self-supervised module to supervise the embedding and clustering module. However, the above models have the following limitations: (1) Existing models are limited by the calculation method of graph convolution, and their computational costs will increase exponentially as the scale of the graph grows. (2) Stacking too many convolutional layers will introduce the over-smoothing noises and ignore the local graph structure (3) The model depth is orthogonal to the neighborhood range, which makes it difficult to expand both. Therefore, researchers expect to find more scalable models. [PERSON] et al. [12] propose a simple model using the relation between graph convolution and pagerank, which enables an efficient neighborhood expansion. [PERSON] et al. [13] entirely reduce the computational costs by decoupling the feature propagation from the training process. Following the idea of SGC, [PERSON] et al. [14] consider the features of different receptive layers and splice them without ignoring information, while [PERSON] et al. [15] average them to generate combined features with the same dimension. Meanwhile, [PERSON] et al. [16] simplify the GNN from the perspective of spectral graph theory and it can select different high-order information orders according to different graphs. Despite this, the above models ignore the difference in node importance in the aggregation process. [PERSON] et al. [17] adopt a constant decay factor to solve this issue, while [PERSON] et al. [18] use the receptive field weighted aggregation with an attention mechanism to aggregate neighborhood information. However, the above methods are suitable for supervised or semi-supervised learning scenarios, lacking a task-oriented model framework for unsupervised clustering tasks.