# Degree-Mass Message Passing for Betweenness Ranking in Directed and Undirected Networks

arXiv: https://arxiv.org/abs/2602.09716 · HTML: https://mlsanity.com/paper/2602.09716/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 10 Feb 2026.

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

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Learning to Identify High Betweenness Centrality Nodes from Scratch: A Novel Graph Neural Network Approach](https://mlsanity.com/paper/1905.10418/) (2019)
- [Scaling betweenness centrality using communication-efficient sparse matrix multiplication](https://mlsanity.com/paper/1609.07008/) (2016)
- [Efficient Approximation Algorithms for Spanning Centrality](https://mlsanity.com/paper/2305.16086/) (2023)
- [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)
- [SILVAN: Estimating Betweenness Centralities with Progressive Sampling and Non-uniform Rademacher Bounds](https://mlsanity.com/paper/2106.03462/) (2021)
- [Correlation between centrality metrics and their application to the opinion model](https://mlsanity.com/paper/1409.6033/) (2014)
- [Algorithms and Heuristics for Scalable Betweenness Centrality Computation on Multi-GPU Systems](https://mlsanity.com/paper/1602.00963/) (2016)
- [Scalable Betweenness Centrality Maximization via Sampling](https://mlsanity.com/paper/1609.00790/) (2016)
- [Querying Probabilistic Neighborhoods in Spatial Data Sets Efficiently](https://mlsanity.com/paper/1509.01990/) (2015)
- [Making Temporal Betweenness Computation Faster and Restless](https://mlsanity.com/paper/2501.12708/) (2025)

## Built on by (most cited first, 1 of 1)

- [Graph Neural Networks for Scalable and Transferable Node Centrality Approximation](https://mlsanity.com/paper/2607.09372/) (2026)

## Abstract (arXiv)

Computing the importance of nodes in networks is a long-standing fundamental problem that has driven extensive study of various centrality measures. A particularly well-known centrality measure is betweenness centrality, whose exact computation becomes prohibitive on large-scale networks. Graph Neural Network (GNN) models have thus been proposed to predict the ranking of nodes by betweenness centrality. However, existing GNN-based methods either have graph-size-dependent parameter counts or are limited to undirected graphs. We propose a lightweight GNN architecture that exploits the empirically observed relationship between betweenness centrality and multi-hop degree mass. This motivates the use of degree masses as size-invariant node features. To improve generalization, we train on synthetic graphs whose degree distributions more closely match those of real-world networks, including directed and undirected scale-free graphs and uniformly directed hyperbolic random graphs. We evaluate our model on 14 real-world networks spanning eight domains, including social, email, and citation networks, across both directed and undirected regimes. The experiments show that our model improves the Kendall τb correlation by up to 24.6% on undirected and 10.9% on directed graphs, while using 56× fewer parameters than the lightest competing GNN baseline and achieving competitive inference time, with up to a 24.5× speedup on selected directed graphs.