[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82323-en":3,"doc-seo-82323-105":29,"detail-sidebar-cat-0-en-105":94},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82323,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Graph Neural Networks for Scalable and Transferable Node Centrality Approximation","Graph Neural Networks (GNNs) provide a learning-based framework for approximating graph quantities that are expensive to compute exactly. This work investigates GNNs for scalable approximation of betweenness and closeness centrality, cast as supervised node-ranking using exact centrality labels. Ranking quality is measured with Kendall’s τ correlation, with models evaluated on unseen Erdős–Rényi graphs and cross-topology generalization. Mixed-distribution training improves betweenness transfer, while closeness remains more topology-sensitive and shows reduced generalization. GNN inference offers up to a 97.7× speedup over exact computation.","arXiv :2607 .09372v 1 [ cs .LG] 10 Jul 2026  \nGraph Neural Networks for Scalable and Transferable Node Centrality Approximation  \nSamra Sanaa,b,∗, Giorgio Manticaa , Saul Imbricia  \na Center for Nonlinear and Complex Systems, Università degli Studi  \ndell’Insubria, Como, Italy  \nb Data Science Institute, Hasselt University, Hasselt, Belgium  \n\n| Abstract\u003Cbr>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 τ 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 Erdős– Rényi graphs, the proposed models achieve τ = 0 .851 for betweenness and τ = 0 .894 for closeness. A large-scale betweenness model trained on graphs with N = 5 ,000 nodes achieves τ = 0 .938, demonstrating scalability. Mixeddistribution training on Erdős–Rényi, Barabási–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 97.7× 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.\u003Cbr>Keywords: Graph Neural Networks, centrality approximation, node\u003Cbr>ranking, transfer learning, graph representation learning, complex networks |\n| --- |\n|  |\n\n∗ Corresponding author  \nEmail address: [samra.sana@studenti.uninsubria.it](samra.sana@studenti.uninsubria.it) (Samra Sana)  \n1. Introduction  \nGraph Neural Networks (GNNs) have become an important class of learning systems for graph-structured data. By combining local message passing with trainable nonlinear transformations, GNNs can learn node representations that support tasks such as node classification, link prediction, graph classification, and ranking. Beyond standard prediction tasks, GNNs are increasingly used as neural approximators for graph algorithms, where the objective is to learn graph quantities that are expensive to compute exactly. Node centrality approximation is a natural and challenging problem in this setting. Centrality measures quantify the structural importance of nodes in a graph and are widely used in social, biological, transportation, communication, and recommendation networks [1] . Among them, betweenness centrality measures how often a node lies on shortest paths between other nodes and is associated with brokerage or control of information flow [2] . Closeness centrality measures how efficiently a node can reach the rest of the network [3 , 1] . However, exact computation of these measures becomes expensive for large graphs, especially for betweenness centrality, which requires repeated shortest-path computations.  \nThis computational cost motivates learning-based approximation methods that can preserve centrality-induced node rankings while reducing inference time. In this work, we formulate betweenness and closeness centrality approximation as supervised node-ranking problems. Instead of reproducing exact centrality values, the goal is to learn the ranking induced by exact centrality measures, as illustrated in Figure 1. This formulation is suitable for many applications in which the relative importance of nodes is more relevant than the exact numerical centrality score.  \nFigure 1: Goal: approximate the ranking induced by exact betweenness and closeness centrality.  \nMessage-passing GNNs provide a data-driven frame","cbCaigTCZpdfv0gC","https://ap.wps.com/l/cbCaigTCZpdfv0gC","pdf",3061959,1,22,"English","en",105,"# Introduction\n## Contributions","[{\"question\":\"How does the paper formulate centrality approximation for GNNs?\",\"answer\":\"It formulates betweenness and closeness centrality approximation as supervised node-ranking problems, using exact centrality values as supervision rather than targeting exact numeric scores.\"},{\"question\":\"What metric is used to evaluate ranking quality?\",\"answer\":\"Ranking quality is evaluated using Kendall’s τ rank correlation between the predicted and exact centrality-induced rankings.\"},{\"question\":\"Does mixed-distribution training help generalize across different graph families?\",\"answer\":\"Yes. Mixed-distribution training across Erdős–Rényi, Barabási–Albert, and Gaussian Random Partition graphs improves betweenness transfer across graph families.\"},{\"question\":\"How does GNN inference speed compare to exact centrality computation?\",\"answer\":\"The paper reports up to a 97.7× speedup over exact computation during GNN inference.\"}]",1784179623,55,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":89,"head_meta":91,"extra_data":93,"updated_unix":27},"graph-neural-networks-for-scalable-and-transferable-node-centrality-approximation","",{"@graph":35,"@context":88},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/graph-neural-networks-for-scalable-and-transferable-node-centrality-approximation/82323/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80,84],{"name":71,"@type":72,"acceptedAnswer":73},"How does the paper formulate centrality approximation for GNNs?","Question",{"text":74,"@type":75},"It formulates betweenness and closeness centrality approximation as supervised node-ranking problems, using exact centrality values as supervision rather than targeting exact numeric scores.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What metric is used to evaluate ranking quality?",{"text":79,"@type":75},"Ranking quality is evaluated using Kendall’s τ rank correlation between the predicted and exact centrality-induced rankings.",{"name":81,"@type":72,"acceptedAnswer":82},"Does mixed-distribution training help generalize across different graph families?",{"text":83,"@type":75},"Yes. Mixed-distribution training across Erdős–Rényi, Barabási–Albert, and Gaussian Random Partition graphs improves betweenness transfer across graph families.",{"name":85,"@type":72,"acceptedAnswer":86},"How does GNN inference speed compare to exact centrality computation?",{"text":87,"@type":75},"The paper reports up to a 97.7× speedup over exact computation during GNN inference.","https://schema.org",{"og:url":51,"og:type":90,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":92,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":95},[96,100,104,108,113,118,123,126,131,134,138],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":105,"show_sort_weight":106,"slug":107},"Exam",70,"exam",{"id":109,"doc_module":4,"doc_module_name":45,"category_name":110,"show_sort_weight":111,"slug":112},5,"Comic",60,"comic",{"id":114,"doc_module":4,"doc_module_name":45,"category_name":115,"show_sort_weight":116,"slug":117},6,"Technology",50,"technology",{"id":119,"doc_module":4,"doc_module_name":45,"category_name":120,"show_sort_weight":121,"slug":122},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":124,"slug":125},30,"research-report",{"id":127,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":129,"slug":130},9,"Religion & Spirituality",20,"religion-spirituality",{"id":129,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":129,"slug":133},"World Cup","world-cup",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":135,"slug":137},10,"Lifestyle","lifestyle",{"id":139,"doc_module":4,"doc_module_name":45,"category_name":140,"show_sort_weight":109,"slug":141},19,"General","general"]