GNNs Improve Scalable and Transferable Node Centrality Approximation

Calculating exact node centrality measures like betweenness and closeness in large graphs is computationally expensive. Graph Neural Networks (GNNs) offer a learning-based alternative for approximating these quantities, framing it as a node-ranking problem. This research investigates the ability of message-passing GNNs to learn transferable structural representations across different graph topologies, rather than just fitting the training distribution. Using exact centrality values as supervision, the GNN models achieved high Kendall's tau rank correlation scores: 0.851 for betweenness and 0.894 for closeness on unseen Erdos-Renyi graphs. A large-scale betweenness model trained on graphs with 5,000 nodes demonstrated scalability with a tau of 0.938. Mixed-distribution training, involving Erdos-Renyi, Barabasi-Albert, and Gaussian Random Partition graphs, significantly improved betweenness transfer across different graph families. However, closeness centrality proved more sensitive to community-structured graphs and showed reduced transferability to real-world topologies. Crucially, GNN inference achieved up to a 97.7x speedup compared to exact centrality computation, highlighting their practical utility for large-scale graph analysis.