Robust Contrastive Graph Clustering with Adaptive Local-Global Integration

1 Introduction

Graph clustering is a fundamental task in graph analysis ever, aiming to partition nodes into clusters or communities based on structural attributes or connectivity patterns, which is essential for uncovering underlying patterns and relationships among nodes. This task has been studied and applied in domains including social network analysis [Qiu et al., 2018], knowledge graphs [Bellomarini et al., 2022], and recommender systems [Fan et al., 2019; Wu et al., 2025a]. As a long-standing research topic, graph clustering continues to evolve.

∗Corresponding Author.

To advance deep graph clustering, Graph Convolutional Networks (GNNs) [Kipf and Welling, 2016] have been employed to learn node representations through message passing. Building on this, self-supervised graph representation learning has emerged as a promising paradigm, leveraging intrinsic structural and attribute information as supervisory signals to guide similar nodes toward compact embeddings. Existing approaches typically follow generative or contrastive paradigms. Generative methods reconstruct graph topology and features via an encoder-decoder architecture, with enhancements combining MLPs and GCNs to capture semantic and structural cues [Tu et al., 2021]. In contrast, contrastive learning constructs positive and negative sample pairs to maximize mutual information between positives while minimizing it for negatives [Peng et al., 2024].

Despite significant advances in deep graph clustering, most existing methods focus primarily on local neighborhood aggregation while overlooking the integration of high-order local structures and global context. This often results in unstable and suboptimal node embeddings, especially in realworld graphs where cluster boundaries are ambiguous. Nodes situated near community intersections or in fragmented subgraphs face particular challenges: they require adaptive fusion of multi-scale neighborhood information across shallow and deep receptive fields, but conventional message passing either ignores this heterogeneity or introduces noise from distant nodes. Moreover, many real-world graphs are fragmented, leaving isolated or weakly connected components with limited access to high-level contextual signals and making cross-community discrimination unreliable. Without global awareness, long-range dependencies become fragile and embeddings for such nodes may collapse. In this work, a basic clustering pipeline is adopted in which GNN-based encoders produce node embeddings that are clustered by kmeans; however, as high-betweenness edges are removed, clustering performance further deteriorates (see Figure 1).

To address these limitations, this paper proposes a novel graph clustering framework that jointly integrates multi-scale local structural information and global semantic prototypes in an adaptive manner. At the local level, node representations with different receptive fields are fused through a purpose-built multi-head attention mechanism rather than a generic combination of GNN and attention. Specifically, features from different propagation layers are aggregated via max-pooling and scaled dot-product attention, enabling each node to selectively absorb relevant shallow or deep neighborhood cues. This design directly alleviates the over-smoothing and noise accumulation problems in rigid message-passing schemes, while improving the ability to capture hierarchical structural patterns. At the global level, dynamically updated cluster centers act as semantic prototypes. Through a cluster-guided attention mechanism, nodes selectively integrate global signals that evolve with the latent clustering structure. Unlike static global aggregation, this dynamic strategy adapts to structural changes and is particularly beneficial for nodes in sparse or fragmented regions, addressing the unreliability of long-range dependencies in real-world graphs. This dual-level integration enables the model to handle both local structural ambiguity and global fragmentation.

In addition, the framework adopts a contrastive learning paradigm by generating two augmented graph views to enable label-free representation learning. This is particularly important in unsupervised graph clustering, where the absence of ground-truth labels often leads to collapsed node representations. By enforcing consistency between different views of the same node (via instance-level contrastive loss) and leveraging graph topology to align structural neighbors (via neighbor-supervised loss), the model mitigates collapse and enhances structural discrimination. Consequently, this hybrid training objective yields embeddings that are more robust and consistent, and generalize better across diverse graphs. The main contributions of this work are summarized as follows:

• We propose RCLG, a robust contrastive graph clustering framework that integrates multi-scale local structural cues with global semantic context via attention mechanisms under a dual-view self-supervised paradigm.
• We introduce two complementary components for localglobal integration: a multi-head attention-based local fusion module that adaptively weights multi-depth representations, and a prototype-guided global aggregation module that uses dynamic cluster centers to inject global context and improve inter-cluster separability in sparse

or fragmented graphs.

• The proposed model demonstrates strong robustness and stability. Without the need for dataset-specific hyperparameter tuning, it achieves consistently competitive clustering performance across diverse graph datasets with varying structures, highlighting its practical utility and deployment-friendliness.

2 RelatedWork

This section reviews the literature from two key perspectives. The first part surveys the landscape of Deep Graph Clustering, providing foundational context for this research. The second part examines a key challenge in this domain: effective capture of Long-range Dependencies in Graphs, analyzing the capabilities and limitations of existing approaches.

2.1 Deep Graph Clustering

Deep graph clustering aims to partition graph nodes into meaningful communities by leveraging deep neural networks to jointly capture both node attributes and structural dependencies [Zhao et al., 2025]. With the introduction of GNNs, this task has witnessed significant progress, as GNNs offer a natural way to propagate and fuse feature information over graph topology. By extending the principles of deep clustering, graph-based approaches no longer treat each sample in isolation but instead emphasize the relational structure among nodes, enabling more coherent clustering decisions.

Graph contrastive learning (GCL) [Xu et al., 2021; Xia et al., 2022] is a self-supervised learning method that has been widely studied in various research areas [Zhang et al., 2022; Zheng et al., 2025], such as node classification, recommendation, and clustering. Inspired by the success of GCL in self-supervised representation learning, several works have adopted GCL-based techniques to enhance cluster separability in an unsupervised manner [Devvrit et al., 2022; Ma and Zhan, 2023; Yang et al., 2023; Peng et al., 2025]. Models such as SCGC and RGC initiate clustering by employing shallow graph convolutions to encode local interactions, followed by contrastive learning to capture relational patterns among samples. However, their shallow architectures limit the expressiveness of node embeddings, especially in capturing complex dependencies, which hinders clustering performance.

To address this, methods like SDCN [Bo et al., 2020] and AGCN [Peng et al., 2021] introduce deeper GNN architectures and attribute-structure fusion mechanisms to refine representation quality. These approaches demonstrate that deeper propagation can enrich the semantic content of node embeddings and better capture latent cluster structures. Nevertheless, they still suffer from limitations such as rigid neighborhood aggregation and inadequate handling of higher-order local information. Specifically, they often apply uniform message passing schemes across the graph, which can lead to noise accumulation or oversmoothing, particularly for nodes near community boundaries or in fragmented subgraphs.

2.2 Long-range Dependencies in Graphs

Capturing long-range dependencies is critical in graph learning, particularly for clustering tasks where nodes within the same community may be distant in the graph topology. Early methods, such as JKNet [Xu et al., 2018] and DAGNN [Liu et al., 2020], attempt to aggregate information using layerwise skip connections or adaptive weighted mechanisms to capture local features. BM-GCN [He et al., 2022] and HOGGCN [Wang et al., 2022] consider all neighbors to aggregate global information. However, these methods rely on the original graph topology, which makes them vulnerable to the influence of structural noise or sparsity in the graph.

Recently, MGCN [Li et al., 2024] demonstrates the effectiveness of adaptively fusing multi-layer receptive field information for graph clustering. By incorporating deeper neighborhood contexts, it enables the aggregation of higher-order local structural information, beneficial for capturing nuanced intra-cluster relationships. However, these approaches typically rely on the assumption that the input graph is wellconnected. In real-world scenarios, graphs are often fragmented, exhibiting isolated or weakly connected components. In such fragmented structures, traditional message-passing mechanisms either fail to transmit meaningful global signals or suffer from excessive noise introduced by irrelevant paths. As a result, embeddings of nodes-especially those in sparse regions-become unstable and less discriminative. Although DGAC [Xie et al., 2025] is capable of capturing high-order semantic information, it can only marginally handle the issue of missing edges in the original graph. Therefore, effective local integration of higher-order structural information and strong global semantic guidance are both crucial for robust clustering, especially under sparse or fragmented graph connectivity.

3 Methodology

3.1 Overview

We use the following notations throughout this paper. An undirected graph is defined as G = (V,E), where V = {v1, v2, . . . , vN} denotes the set of N nodes and E ⊆ V ×V is the edge set. The node features are represented by the matrix X ∈ RN×d , where d is the input feature dimension. The structure of the graph is described by the adjacency matrix A ∈ {0, 1}N×N , where Aij = 1 if an edge exists between nodes vi and vj, and Aij = 0 otherwise. The degree matrix is denoted as D ∈ RN×N , where each diagonal element Dii equals the degree of node vi. Incorporating self-loops involves defining ˜ A = A+I and ˜D =D+I, with I representing the identity matrix. Given an unlabeled graph G = (V, E) with node features X, graph clustering aims to partition the nodes into K disjoint clusters, denoted by an assignment vector y ∈ {1, . . . , K}N , such that nodes within the same cluster are highly similar while nodes from different clusters are well separated in the learned representation space.

In this section, the proposed model framework for addressing the above problem is introduced. As shown in Figure 2, the method adopts a contrastive learning framework composed of two structurally identical views. For each view, input node features are first encoded, followed by local and global information integration through multi-head attention. This design captures multi-scale structural information and enhances representation robustness. Unless otherwise specified, the following subsections describe the node representation learning process from the perspective of a single view, denoted as view e (where e = 1 or 2). In what follows, the framework is introduced component by component starting from view construction at the input stage, then detailing local and global fusion modules, and finally presenting the overall training objective.

3.2 Noise-based ViewAugmentation for Robust Contrastive Learning

To improve the robustness of node representations and enhance contrastive learning, Gaussian noise is injected during feature encoding. Given the input node feature matrix X, view-specific embeddings are generated by applying an MLP followed by noise addition:

where Z ve ∈ RN×d denotes the embeddings for view e, α controls the noise level, and ε is standard Gaussian noise. This formulation preserves structural consistency while introducing feature perturbations, promoting harder positives and preventing collapse.

Unlike graph-specific augmentations such as edge dropping or diffusion-which are often complex and datasetsensitive-this feature-space augmentation is simple, efficient, and broadly applicable [Liu et al., 2023]. It offers a lightweight yet effective means of generating distinct but semantically consistent views, facilitating robust contrastive learning in subsequent fusion stages.

3.3 Multi-level Local Feature Fusion via Attention

To capture multi-scale local structural information, repeated message passing is performed over the noisy node embeddings Z ve using the normalized adjacency matrix ˆ A. Specifically, for each propagation step t, the corresponding layerwise representation Ht is computed, and all such representations are stacked to obtain a multi-layer feature tensor S:

where ˆ A = ˜D- 1 2 ˜ A ˜D- 1 2 is the symmetrically normalized adjacency matrix, Z ve ∈ RN×d denotes the initial node embeddings in view ve, Ht is the node representation after t-hop propagation, and S is the resulting stacked tensor comprising multi-scale representations for each node.

To adaptively select the most informative layer-wise features for each node, max-pooling is applied across all Ht, followed by a linear transformation to obtain the query matrix for attention weighting.

where (max1≤t≤l Ht) denotes the maximum across all layers for each dimension, and W qL ∈ Rd×d is a learnable matrix transforming pooled features into query vectors for attention.

A scaled dot-product attention mechanism is employed to compute the attention weights between QL and each layer in S, and the resulting scores are used to aggregate the layerwise representations. A residual connection and layer normalization are applied to obtain the locally fused embeddings Z ve L :

where dh is hidden dimension for scaled attention, and Z ve is the residual input for stabilization. The function LayerNorm(·) normalizes the output to improve training.

This adaptive fusion strategy enables each node to selectively integrate signals from various receptive field depths, improving the quality and robustness of local representations.

3.4 Global Semantic Aggregation

To supplement local representations with semantic-level global context, we introduce a cluster-aware global aggregation mechanism. A set of cluster centers, as global semantic prototypes, is dynamically updated. These centers are computed by applying a clustering algorithm (e.g., K-Means [Hartigan and Wong, 1979] or spectral clustering [Von Luxburg, 2007]) to fused node representations Z ve L :

where Ce denotes the set of k cluster centers derived from the current view e, Φ denotes a clustering algorithm and each center represents a global semantic anchor corresponding to a latent cluster.

To incorporate global semantics into node-level representations, a multi-head attention mechanism [Vaswani et al., 2017] is used. In this process, node embeddings and global context are linearly projected and reshaped into multiple attention heads, forming the query, key, and value matrices:

where W qG ∈ Rd×d is a learnable projection matrix for transforming node embeddings into queries, and Z ve L ∈ Rn×d represents the locally fused node embeddings from view ve.

Scaled dot-product attention is then applied between each node and the cluster centers, enabling nodes to selectively attend to global semantic prototypes:

where QG, K, and V are the query, key, and value matrices as defined in the previous step; dh denotes the dimensionality of each attention head.

Subsequently, a residual connection is formed between the global aggregated output and the locally fused representation, followed by layer normalization:

where β ∈ [0, 1] is a coefficient controlling the trade-off between global and local signals.

This global semantic aggregation mechanism strengthens node embeddings by incorporating high-level structural prototypes from the entire graph. Such enhancement is especially advantageous for nodes situated in weakly connected or isolated components, where local message passing is often insufficient for capturing informative global context.

3.5 Representation Learning and Clustering Objective

To obtain discriminative and semantically rich node representations, the representation learning loss Lr consists of an instance-level contrastive term LinfoNEC and a neighborsupervised term Lns.

The instance-level contrastive loss follows the InfoNCE principle, aiming to pull together representations of the same node across two augmented views while pushing apart representations of other node pairs. Given embeddings from the two augmented views Z ve G and Z vf G , the similarity between two nodes is defined as:

where Z ve Gi and Z vf Gj are the normalized embeddings of nodes i and j in views ve and vf , respectively.

The instance-level InfoNCE loss is then given by:

where Lve i denotes the contrastive loss for node i in view ve, and N is the number of nodes.

To further incorporate structural signals, Lns is introduced. This term enforces similar embeddings for neighboring nodes based on the binarized normalized adjacency matrix ˜ A:

where ˜aij indicates the presence of an edge between nodes i and j.

The combined representation learning loss is defined as:

Beyond improving embedding quality, a clustering alignment loss Lclu is adopted to enhance clustering performance, inspired by previous works [Guo et al., 2017; Wang et al., 2019a; Xie et al., 2016]. This term aligns the soft cluster assignments q with a sharpened target distribution p, and is typically optimized using KL divergence.

Combining all components, the final training objective is:

where γ is a hyperparameter controlling the influence of the clustering objective.

4 Experiments

This section presents a comprehensive evaluation of the proposed model from multiple perspectives. It begins by introducing benchmark datasets, evaluation metrics, and experimental setup. The clustering results of RCLG are compared with state-of-the-art baselines, followed by analyses of RCLG variants, including ablation studies and hyperparameter sensitivity experiments. Experiments were conducted on a workstation with an NVIDIA RTX 4090 GPU.

4.1 Benchmark Datasets and and Evaluation Metrics

The evaluation is conducted on eight widely used real-world graph datasets with diverse structures and domains, covering air-traffic networks (UAT [Mrabah et al., 2022]), word co-occurrence graphs (Wiki), citation networks (Cora [Cui et al., 2020] and Citeseer [Cui et al., 2020]), e-commerce co-purchase graphs (AMAP [Liu et al., 2022]), and academic co-authorship networks (ACM [Wang et al., 2019b], DBLP [Wang et al., 2019b], and COCS [Shchur et al., 2018]). Dataset statistics are summarized in Table 1. Clustering performance is evaluated using three widely adopted metrics: Accuracy (ACC), Normalized Mutual Information (NMI), and macro F1-score (F1).

4.2 Baselines and Experimental Setup

Eight representative graph clustering methods are selected for comparison, including traditional structure modeling approaches and contrastive learning-based methods. Specifically, AGC [Zhang et al., 2019] employs adaptive graph convolution to model global structural information. SDCN [Bo et al., 2020] integrates node attributes and structure in a unified clustering framework. FGC [Kang et al., 2022] proposes a fine-grained strategy for attribute graph clustering. VGAER [Qiu et al., 2022] utilizes variational inference to jointly model topology and attributes. AGC-DRR [Gong et al., 2022] designs a redundancy-reduced representation learning method. In addition, recent contrastive learning-based methods are considered, including SCGC [Liu et al., 2023] which focuses on efficient neighbor contrast, MAGI [Liu et al., 2024] which leverages modularity, MCGC [Wu et al., 2025b] addressing motif-based contrastive clustering, and WGCN [Wang et al., 2026] which adopts a representationthen-augmentation framework.

The model is trained with learning rate lr = 5 × 10-4 for 500 epochs. The noise perturbation coefficient is set to α = 0.01, and the clustering update interval is T = 5. The global semantic fusion coefficient is β = 0.2, and the clustering alignment loss is weighted by γ = 10. The hidden representation dimensionality is 256, and the number of graph propagation steps is l = 6. For baselines, the best configuration is individually selected for each dataset, whereas our method uses a single fixed configuration across all datasets.

4.3 Clustering Performance Comparisons

As shown in Table 2, the proposed method exhibits particularly notable improvements on larger-scale datasets. Specifically, on the AMAP dataset, a relative accuracy improvement of approximately 5.88% is achieved compared to the secondbest approach, while on the COCS dataset, the improvement reaches 7.40%. These results indicate that integrating local and global information becomes increasingly effective as the dataset scale increases. Moreover, the method is robust to varying sparsity. Table 1 reports that Wiki and ACM are relatively denser (0.0029), whereas DBLP (0.0004) and COCS (0.0005) are among the sparsest datasets; nevertheless, strong performance is consistently achieved, indicating reliable clustering under sparse or fragmented connectivity.

4.4 Ablation Study

To analyze the contribution of each key component and mechanism, ablation studies are conducted on different model variants. Specifically, w/o A denotes removing all attention mechanisms: attention is replaced with mean fusion in the local component, and equal weights are assigned to all cluster centers in the global component. w/o L&G denotes the variant that performs simple mean fusion of multi-scale representations without the global information integration module. w/o G removes only the global information integration component, while RCLG represents the full model. As shown in Table 3, on the Wiki dataset, the integration of local information improves clustering performance with a relative enhancement of 7.1%. On the Cora dataset, incorporating global information yields a relative improvement of 1.7%. These findings demonstrate that both local and global information integration modules substantially enhance the overall framework's effectiveness.

In addition, Table 4 presents the effect of the two components constituting the representation learning loss LR. The results indicate that both the instance-level contrastive loss LinfoNEC and the neighbor-supervised contrastive loss Lns contribute to improving clustering performance. Among them, LinfoNEC plays a more prominent role by ensuring fundamental discriminability between node embeddings, which is particularly beneficial for enhancing clustering quality.

4.5 Impact of Clustering AlgorithmChoice

To examine the effect of the clustering algorithm, we assess whether the Global component is sensitive to the choice of method. The Global module only requires reliable cluster centers to deliver global information via attention, and these centers are treated as learnable parameters updated jointly with the model, reducing dependence on random initialization and enhancing robustness.

To validate this, we replaced the default clustering algorithm with Spectral Clustering. As shown in Table 5, the replacement has little impact on performance. Across datasets, Spectral Clustering and our original RCLG achieve comparable results, confirming that the model is not tied to a specific clustering algorithm and remains robust and effective.

4.6 Sensitivity Analysis

To further assess model robustness, sensitivity analysis is performed on three hyperparameters: noise coefficient α, global fusion coefficient β, and propagation layers l.

As shown in Figure 3, setting the noise coefficient α to 0.01 yields stable and strong performance across multiple datasets, demonstrating the effectiveness of introducing mild noise to enhance representation robustness. Likewise, Table 6 shows that within the range β ∈ [0.2, 0.4], each dataset tends to achieve its optimal performance, indicating that the model remains robust and broadly applicable when balancing global and local information in this interval. When either α or β is set excessively high, clustering performance degrades on several datasets, suggesting that overly strong perturbations or global dependencies may overwhelm local learning. This confirms the necessity of maintaining a balanced integration between local and global information.

Furthermore, as summarized in Table 7, datasets with larger diameters generally reach best performance at slightly deeper propagation steps, reflecting the need for sufficient receptive field expansion to capture long-range dependencies. Considering both accuracy and efficiency, we fix the propagation depth to l = 6 in all subsequent experiments.

4.7 Computational Efficiency

To further assess the practicality of our method, we compared the per-epoch runtime of RCLG with several stateof-the-art baselines on three representative datasets, namely COCS (18,333 nodes), AMAP (7,650 nodes), and ACM (3,025 nodes). As summarized in Figure 4, the runtime of RCLG is of the same order of magnitude as other methods, indicating that the improved clustering performance does not incur excessive computational overhead. This suggests that our framework achieves competitive efficiency while maintaining superior clustering quality.

5 Conclusion

This paper presents a robust contrastive graph clustering framework that leverages both local and global structural signals within a dual-view architecture to address key limitations. A multi-level attention fusion aggregates neighborhood information from multiple convolutional layers, allowing each node to selectively absorb informative cues across depths and reducing noise from rigid message passing. Semantic prototypes from evolving cluster centers further provide global guidance, enabling nodes-especially in sparse or disconnected regions-to incorporate context beyond immediate neighbors, stabilizing long-range semantics and strengthening cross-community discrimination. Together, these mechanisms improve representation quality and promote more compact and separable clusters. The framework achieves strong performance across diverse benchmarks without dataset-specific hyperparameter tuning.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61976001, 62502340), the Natural Science Foundation of Anhui Province (No. 2408085MF152, 2508085MF176) and the Natural Science Foundation of Tianjin (No. 24JCQNJC01560).