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

arXiv: https://arxiv.org/abs/2509.02609 · HTML: https://mlsanity.com/paper/2509.02609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 30 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [Hard Sample Aware Network for Contrastive Deep Graph Clustering](https://mlsanity.com/paper/2212.08665/) (2022)
- [Cluster-guided Contrastive Graph Clustering Network](https://mlsanity.com/paper/2301.01098/) (2023)
- [Simple Contrastive Graph Clustering](https://mlsanity.com/paper/2205.07865/) (2022)
- [Dink-Net: Neural Clustering on Large Graphs](https://mlsanity.com/paper/2305.18405/) (2023)
- [Deep Incomplete Multi-view Clustering with Cross-view Partial Sample and Prototype Alignment](https://mlsanity.com/paper/2303.15689/) (2023)
- [CONVERT:Contrastive Graph Clustering with Reliable Augmentation](https://mlsanity.com/paper/2308.08963/) (2023)
- [DealMVC: Dual Contrastive Calibration for Multi-view Clustering](https://mlsanity.com/paper/2308.09000/) (2023)
- [Revisiting Modularity Maximization for Graph Clustering: A Contrastive Learning Perspective](https://mlsanity.com/paper/2406.14288/) (2024)
- [Reliable Node Similarity Matrix Guided Contrastive Graph Clustering](https://mlsanity.com/paper/2408.03765/) (2024)

## Abstract (arXiv)

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 (textitregular textitequivalence-based textitcontrastive textitclustering), 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.