  Graph clustering, which involves the partitioning of nodes within a graph
into disjoint clusters, holds significant importance for numerous subsequent
applications. Recently, contrastive learning, known for utilizing supervisory
information, has demonstrated encouraging results in deep graph clustering.
This methodology facilitates the learning of favorable node representations for
clustering by attracting positively correlated node pairs and distancing
negatively correlated pairs within the representation space. Nevertheless, a
significant limitation of existing methods is their inadequacy in thoroughly
exploring node-wise similarity. For instance, some hypothesize that the node
similarity matrix within the representation space is identical, ignoring the
inherent semantic relationships among nodes. Given the fundamental role of
instance similarity in clustering, our research investigates contrastive graph
clustering from the perspective of the node similarity matrix. We argue that an
ideal node similarity matrix within the representation space should accurately
reflect the inherent semantic relationships among nodes, ensuring the
preservation of semantic similarities in the learned representations. In
response to this, we introduce a new framework, Reliable Node Similarity Matrix
Guided Contrastive Graph Clustering (NS4GC), which estimates an approximately
ideal node similarity matrix within the representation space to guide
representation learning. Our method introduces node-neighbor alignment and
semantic-aware sparsification, ensuring the node similarity matrix is both
accurate and efficiently sparse. Comprehensive experiments conducted on $8$
real-world datasets affirm the efficacy of learning the node similarity matrix
and the superior performance of NS4GC.
