Node ranking is a fundamental problem in graph information retrieval, measuring the relative importance of nodes and supporting a wide range of applications such as influence analysis, recommendation, and graph-based retrieval augmented generation. However, exact computation of graph-based ranking measures is often computationally prohibitive at scale. Existing GNN-based ranking methods provide scalable approximations, but they are typically tailored to individual ranking criteria and require retraining for each downstream task, which limits their transferability and efficiency. Recent graph pre-training approaches aim to enable knowledge transfer across tasks, yet their learning objectives are largely misaligned with node ranking, resulting in suboptimal adaptability to ranking-oriented applications. To address these limitations, we propose PreGress, the first ranking-native pre-training and prompting framework for supporting a wide range of node ranking tasks. PreGress performs multi-task pre-training using our carefully designed objectives, including degree centrality prediction and attribute reconstruction, to jointly capture structural and attribute information. To support heterogeneous ranking criteria, we design lightweight, task-specific prompt modules that adapt a frozen ranking backbone to downstream tasks without full retraining. Experiments on six public graphs and two real-world query-to-item benchmarks---Yelp2018 and MovieLens-100K---together with a controlled five-criterion graph-access study demonstrate strong ranking quality with low task-specific state overhead.
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.