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.

翻译：计算网络中节点重要性是一个长期存在的基础性问题，推动了各类中心性度量指标的广泛研究。介数中心性作为一种尤为著名的中心性度量，在大规模网络上的计算成本极高。为此，研究者提出了图神经网络模型，以根据节点的相对介数中心性预测其排序。然而，现有最先进方法难以推广至高直径图结构（如道路网络）。本文提出BRAVA-GNN——一种轻量级图神经网络架构，其利用经验观测到的介数中心性与基于度的度量指标（特别是多跳度质量）之间的相关性。这种相关性促使我们将度质量作为尺寸不变的节点特征，并采用与真实网络度分布高度吻合的合成训练图。此外，现有研究多依赖无标度合成图，而本文利用双曲随机图模型——该模型能复现无标度区间外的幂律指数，更好地捕捉道路网络等现实图的结构特性。该设计使BRAVA-GNN能够泛化至多样化的图族，同时参数量比现有最轻量图神经网络基线减少54倍。在涵盖社交网络、网络图、邮件网络和道路图的19个真实网络上的大量实验表明，BRAVA-GNN相比最先进的基于图神经网络的方法，在Kendall-Tau相关性上最高提升214%，推理时间最高加速70倍，尤其在具有挑战性的道路网络上表现突出。