🤖 AI Summary
This study addresses the computational expense of calculating betweenness and closeness centrality for nodes in graphs by reframing the problem as a ranking task and proposing an efficient approximation method based on message-passing graph neural networks. Trained on a diverse mixture of synthetic graphs—including Erdős–Rényi, Barabási–Albert, and Gaussian random partition models—the model demonstrates strong generalization across unseen graph structures, notably enhancing the transferability of betweenness centrality estimates. The work also highlights the sensitivity of closeness centrality to community structure as a key challenge. Experimental results show that the model achieves Kendall’s τ of 0.851 for betweenness and 0.894 for closeness on unseen Erdős–Rényi graphs, and scales effectively to large graphs (N=5000) with τ=0.938 for betweenness, while accelerating inference by up to 97.7× compared to exact computation.
📝 Abstract
Graph Neural Networks (GNNs) provide a learning-based framework for approximating graph quantities that are expensive to compute exactly. This paper investigates GNNs for scalable approximation of betweenness and closeness centrality, formulated as a node-ranking problem. Exact centrality values are used as supervision, and ranking quality is evaluated using Kendall's tau rank correlation. We study whether message-passing GNNs can learn transferable structural representations across different graph topologies rather than only fitting the distribution used during training. On unseen Erdos renyi graphs, the proposed models achieve tau = 0.851 for betweenness and tau = 0.894 for closeness. A large-scale betweenness model trained on graphs with N = 5,000 nodes achieves tau = 0.938, demonstrating scalability. Mixed-distribution training on Erdos renyi, Barabasi-Albert, and Gaussian Random Partition graphs improves betweenness transfer across graph families. In contrast, closeness centrality remains more sensitive to community-structured graphs and shows reduced transfer to real-world topologies. Finally, GNN inference achieves up to a 97.7x speedup over exact computation. These results show that mixed-distribution training can improve structural transfer in GNN-based centrality approximation, while identifying closeness centrality's sensitivity to topology as an open challenge.