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Recently, deep clustering utilizing Graph Neural Networks has shown good performance in the graph clustering. However, the structure information of graph was underused in existing deep clustering methods. Particularly, the lack of concern on mining different types structure information simultaneously. To tackle with the problem, this paper proposes a G raph C lustering Network with S tructure E mbedding E nhanced (GC-SEE) which extracts nodes importance-based and attributes importance-based structure information via a feature attention fusion graph convolution module and a graph attention encoder module respectively. Additionally, it captures different orders-based structure information through multi-scale feature fusion. Finally, a self-supervised learning module has been designed to integrate different types structure information and guide the updates of the GC-SEE. The comprehensive experiments on benchmark datasets commonly used demonstrate the superiority of the GC-SEE. The results showcase the effectiveness of the GC-SEE in exploiting multiple types of structure for deep clustering. • The focus on structural information learned by GCN and GAE varies. • We propose a Graph Clustering Network with Structure Embedding Enhanced (GC-SEE). • GC-SEE integrates different types structure information to enrich the embedding. • A self-supervised loss is designed to achieve clear boundaries and high accuracy. • GC-SEE outperforms the methods using single structure information. [ABSTRACT FROM AUTHOR]