Contrastive clustering based on regular equivalence for influential node identification in complex networks

2025-08-30

AI Summary

To address the challenge of identifying influential nodes in complex networks under unsupervised (label-free) settings, this paper proposes ReCC, an unsupervised deep clustering framework. Methodologically, ReCC innovatively incorporates regular equivalence into contrastive learning for the first time, enabling modeling of higher-order structural similarity beyond immediate neighborhoods—thus eliminating the need for multiple embeddings to generate discriminative positive and negative samples. It jointly optimizes graph reconstruction loss and structural similarity constraints, unifying node representation learning and clustering objectives. Evaluated on multiple benchmark datasets, ReCC consistently outperforms state-of-the-art methods, demonstrating superior accuracy, robustness, and generalizability in fully unsupervised influential node identification.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Identifying influential nodes in complex networks is a fundamental task in network analysis with wide-ranging applications across domains. While deep learning has advanced node influence detection, existing supervised approaches remain constrained by their reliance on labeled data, limiting their applicability in real-world scenarios where labels are scarce or unavailable. While contrastive learning demonstrates significant potential for performance enhancement, existing approaches predominantly rely on multiple-embedding generation to construct positive/negative sample pairs. To overcome these limitations, we propose ReCC ( extit{r}egular extit{e}quivalence-based extit{c}ontrastive extit{c}lustering), a novel deep unsupervised framework for influential node identification. We first reformalize influential node identification as a label-free deep clustering problem, then develop a contrastive learning mechanism that leverages regular equivalence-based similarity, which captures structural similarities between nodes beyond local neighborhoods, to generate positive and negative samples. This mechanism is integrated into a graph convolutional network to learn node embeddings that are used to differentiate influential from non-influential nodes. ReCC is pre-trained using network reconstruction loss and fine-tuned with a combined contrastive and clustering loss, with both phases being independent of labeled data. Additionally, ReCC enhances node representations by combining structural metrics with regular equivalence-based similarities. Extensive experiments demonstrate that ReCC outperforms state-of-the-art approaches across several benchmarks.

Problem

• Unsupervised identification of influential nodes in networks
• Overcoming reliance on labeled data for node influence detection
• Leveraging structural similarity beyond local neighborhoods for contrastive learning

Innovation

• Unsupervised contrastive clustering using regular equivalence
• Graph convolutional network with structural similarity sampling
• Label-free pre-training and fine-tuning with combined losses