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

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.

GraphNeuralNetworks.jl: Deep Learning on Graphs with Julia

GraphNeuralNetworks.jl is an open-source framework for deep learning on graphs, written in the Julia programming language. It supports multiple GPU backends, generic sparse or dense graph representations, and offers convenient interfaces for manipulating standard, heterogeneous, and temporal graphs with attributes at the node, edge, and graph levels. The framework allows users to define custom graph convolutional layers using gather/scatter message-passing primitives or optimized fused operations. It also includes several popular layers, enabling efficient experimentation with complex deep architectures. The package is available on GitHub: \url{https://github.com/JuliaGraphs/GraphNeuralNetworks.jl}.