Limit Analysis of Graph Neural Networks with Wireless Conflict Graphs

Graph neural networks (GNNs) can operate on large graphs but become infrastructure-sensitive at the scale of millions of nodes and typically require scalable training techniques for even larger graphs. This raises a central question: when can a model trained on a smaller, scaled-down replica of a graph be deployed on the full-resolution graph without retraining? We introduce a zero-shot transfer protocol in which a GNN is trained on a graph coarse-grained by geometric renormalization (GR), and the resulting weights are transferred directly to the original network. Across synthetic and real-world networks, training on GR scaled-down replicas preserves much of the original-scale predictive performance while significantly reducing training cost. We further find that learned representations and predictive trajectories remain aligned across scales. These findings suggest that structural similarity may be more important than network size in determining GNN transferability, opening a path toward scale-equivariant graph architectures.

Graph neural networks have moved from a niche representation-learning technique to the default model class wherever data carry relational structure. The interesting question is no longer whether message passing helps on a given dataset, but where graph structure earns its computational cost and where it does not. This survey organises the field around a single design space, derives the spectral and spatial formulations from shared first principles, and connects expressive power to the Weisfeiler-Leman hierarchy with explicit statements of what current architectures can and cannot separate. Against that methodological backbone we examine twelve application domains, among them recommendation and social networks, knowledge graphs and language-model integration, drug discovery and molecular property learning, healthcare and neuroscience, computer vision, traffic and urban computing, power and renewable-energy systems, wireless and sixth-generation networks, fraud and cybersecurity, industrial prognostics, materials science, and climate modelling. For each domain we specify the graph-construction choices and their costs, identify which architecture families dominate and why, and separate reported gains from artefacts of weak baselines or favourable splits. A cross-domain comparison exposes recurring patterns: heterophily and scale undercut the same models almost everywhere, temporal graphs remain harder than their static counterparts, and the architectures that top public leaderboards are seldom the ones that reach deployment. We treat over-smoothing, over-squashing, robustness, distribution shift, fairness, and explainability not as a closing checklist but as the constraints that decide adoption.

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.