BRAVA-GNN: 通过度量质量启发的图神经网络进行介数排名近似
Degree-Mass Message Passing for Betweenness Ranking in Directed and Undirected Networks
AI总结：
BRAVA-GNN通过利用度量质量与介数中心性的相关性，提出了一种轻量级GNN架构，实现对高直径图的高效节点排名近似。
摘要：
在网络中计算节点重要性是一个长期存在的基础问题，推动了各种中心性度量的广泛研究。其中，一个特别著名的中心性度量是介数中心性，但在大规模网络上计算变得计算上不可行。图神经网络（GNN）模型因此被提出，以根据节点的相对介数中心性预测节点排名。然而，最先进的方法无法泛化到高直径图，如道路网络。我们提出了BRAVA-GNN，一种轻量级的GNN架构，利用经验证实的介数中心性与基于度量的量之间的相关性，特别是多跳度量质量。这种相关性促使使用度量质量作为大小不变的节点特征以及与真实网络度分布相似的合成训练图。此外，尽管先前的工作依赖于无标度合成图，我们利用双曲随机图模型，该模型在无标度范围之外再现幂律指数，更好地捕捉现实世界图的结构，如道路网络。这种设计使BRAVA-GNN能够在不同图家族中泛化，同时比最轻量级的现有GNN基线少54倍的参数。在19个现实世界网络上的广泛实验中，涵盖社交、网络、电子邮件和道路图，结果显示，BRAVA-GNN在Kendall-Tau相关性上达到最高214%的提升，并在推理时间上比最先进的GNN方法快70倍，特别是在具有挑战性的道路网络上。
英文摘要：
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 $τ_b$ correlation by up to 24.6\% on undirected and 10.9\% on directed graphs, while using 56$\times$ fewer parameters than the lightest competing GNN baseline and achieving competitive inference time, with up to a 24.5$\times$ speedup on selected directed graphs.
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