# CLGNN: A Contrastive Learning-based GNN Model for Betweenness Centrality Prediction on Temporal Graphs

arXiv: https://arxiv.org/abs/2506.14122 · HTML: https://mlsanity.com/paper/2506.14122/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 55 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys](https://mlsanity.com/paper/1506.03645/) (2015)
- [Contact patterns among high school students](https://mlsanity.com/paper/1409.5318/) (2014)
- [Learning to Identify High Betweenness Centrality Nodes from Scratch: A Novel Graph Neural Network Approach](https://mlsanity.com/paper/1905.10418/) (2019)
- [Can co-location be used as a proxy for face-to-face contacts?](https://mlsanity.com/paper/1712.06346/) (2017)
- [De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs](https://mlsanity.com/paper/2209.08311/) (2022)
- [KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation](https://mlsanity.com/paper/1604.08553/) (2016)
- [Approximating Network Centrality Measures Using Node Embedding and Machine Learning](https://mlsanity.com/paper/2006.16392/) (2020)
- [ABRA: Approximating Betweenness Centrality in Static and Dynamic Graphs with Rademacher Averages](https://mlsanity.com/paper/1602.05866/) (2016)
- [Using Time-Aware Graph Neural Networks to Predict Temporal Centralities in Dynamic Graphs](https://mlsanity.com/paper/2310.15865/) (2023)
- [Label Informed Contrastive Pretraining for Node Importance Estimation on Knowledge Graphs](https://mlsanity.com/paper/2402.17791/) (2024)
- [Algorithmic Aspects of Temporal Betweenness](https://mlsanity.com/paper/2006.08668/) (2020)
- [SILVAN: Estimating Betweenness Centralities with Progressive Sampling and Non-uniform Rademacher Bounds](https://mlsanity.com/paper/2106.03462/) (2021)
- [ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networks](https://mlsanity.com/paper/2203.00653/) (2022)
- [Efficient Top-k Ego-Betweenness Search](https://mlsanity.com/paper/2107.10052/) (2021)
- [Node Centrality Approximation For Large Networks Based On Inductive Graph Neural Networks](https://mlsanity.com/paper/2403.04977/) (2024)
- [A Divide-and-Conquer Algorithm for Betweenness Centrality](https://mlsanity.com/paper/1406.4173/) (2014)
- [Identifying high betweenness centrality nodes in large social networks](https://mlsanity.com/paper/1702.06087/) (2017)

## Abstract (arXiv)

Temporal Betweenness Centrality (TBC) measures how often a node appears on optimal temporal paths, reflecting its importance in temporal networks. However, exact computation is highly expensive, and real-world TBC distributions are extremely imbalanced. The severe imbalance leads learning-based models to overfit to zero-centrality nodes, resulting in inaccurate TBC predictions and failure to identify truly central nodes. Existing graph neural network (GNN) methods either fail to handle such imbalance or ignore temporal dependencies altogether. To address these issues, we propose a scalable and inductive contrastive learning-based GNN (CLGNN) for accurate and efficient TBC prediction. CLGNN builds an instance graph to preserve path validity and temporal order, then encodes structural and temporal features using dual aggregation, i.e., mean and edge-to-node multi-head attention mechanisms, enhanced by temporal path count and time encodings. A stability-based clustering-guided contrastive module (KContrastNet) is introduced to separate high-, median-, and low-centrality nodes in representation space, mitigating class imbalance, while a regression module (ValueNet) estimates TBC values. CLGNN also supports multiple optimal path definitions to accommodate diverse temporal semantics. Extensive experiments demonstrate the effectiveness and efficiency of CLGNN across diverse benchmarks. CLGNN achieves up to a 663.7~× speedup compared to state-of-the-art exact TBC computation methods. It outperforms leading static GNN baselines with up to 31.4~× lower MAE and 16.7~× higher Spearman correlation, and surpasses state-of-the-art temporal GNNs with up to 5.7~× lower MAE and 3.9~× higher Spearman correlation.