BRAVA-GNN: Betweenness Ranking Approximation Via Degree MAss Inspired Graph Neural Network

TL;DR

This work tackles the challenge of efficiently ranking nodes by betweenness centrality on large, high-diameter graphs. It introduces BRAVA-GNN, a lightweight, inductive graph neural network that uses degree-mass features and dual-direction message passing to predict betweenness rankings, trained with hyperbolic random graphs to better reflect real-world topology. The method achieves state-of-the-art ranking accuracy (up to 214% Kendall-$\tau_b$ improvement) and dramatic inference-time speedups (up to 70x) across 19 real networks, while using ~54x fewer parameters than the strongest baselines. The combination of size-invariant degree-mass inputs and hyperbolic training enables robust generalization across diverse graph families, including road networks, with strong qualitative and quantitative support. The work suggests promising future directions for extending the approach to other path-based centralities and temporal graphs.

Abstract

Computing node importance 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, which becomes computationally prohibitive on large-scale networks. Graph Neural Network (GNN) models have thus been proposed to predict node rankings according to their relative betweenness centrality. However, state-of-the-art methods fail to generalize to high-diameter graphs such as road networks. We propose BRAVA-GNN, a lightweight GNN architecture that leverages the empirically observed correlation linking betweenness centrality to degree-based quantities, in particular multi-hop degree mass. This correlation motivates the use of degree masses as size-invariant node features and synthetic training graphs that closely match the degree distributions of real networks. Furthermore, while previous work relies on scale-free synthetic graphs, we leverage the hyperbolic random graph model, which reproduces power-law exponents outside the scale-free regime, better capturing the structure of real-world graphs like road networks. This design enables BRAVA-GNN to generalize across diverse graph families while using 54x fewer parameters than the most lightweight existing GNN baseline. Extensive experiments on 19 real-world networks, spanning social, web, email, and road graphs, show that BRAVA-GNN achieves up to 214% improvement in Kendall-Tau correlation and up to 70x speedup in inference time over state-of-the-art GNN-based approaches, particularly on challenging road networks.

Figures (6)

• Figure 1: Visual comparison on the Jeju Island road network. The predicted rankings (a) closely align with the ground-truth topology (b), demonstrating the model's capability to capture structural importance in high-diameter graphs.
• Figure 2: BRAVA-GNN Architecture Overview. The model utilizes 6-th order degree mass as input features, followed by two message-passing layers with ReLU activation and shared MLPs.
• Figure 3: Inference Time vs Number of Edges for BRAVA-GNN, GNN-Bet, and ABCDE. BRAVA-GNN demonstrates significantly lower inference times across varying graph sizes.
• Figure 4: Rank-rank plots. Comparison between true betweenness rank ($x$-axis) and predicted betweenness rank ($y$-axis). The red dashed line represents the ideal $y=x$ prediction.
• Figure 5: Prediction error on the Ca-NetScience network ($\tau_b=0.8688$), where color indicates the rank delta $\Delta$ between predicted and true rankings.