Node ranking based on graph curvature and PageRank

doi:10.1088/1674-1056/ad9a9b

Abstract Identifying key nodes in complex networks is crucial for understanding and controlling their dynamics. Traditional centrality measures often fall short in capturing the multifaceted roles of nodes within these networks. The PageRank algorithm, widely recognized for ranking web pages, offers a more nuanced approach by considering the importance of connected nodes. However, existing methods generally overlook the geometric properties of networks, which can provide additional insights into their structure and functionality. In this paper, we propose a novel method named Curv-PageRank (C-PR), which integrates network curvature and PageRank to identify influential nodes in complex networks. By leveraging the geometric insights provided by curvature alongside structural properties, C-PR offers a more comprehensive measure of a node’s influence. Our approach is particularly effective in networks with community structures, where it excels at pinpointing bridge nodes critical for maintaining connectivity and facilitating information flow. We validate the effectiveness of C-PR through extensive experiments. The results demonstrate that C-PR outperforms traditional centrality-based and PageRank methods in identifying critical nodes. Our findings offer fresh insights into the structural importance of nodes across diverse network configurations, highlighting the potential of incorporating geometric properties into network analysis.

Keywords: important nodes graph curvature complex networks network geometry

Received: 30 September 2024
Revised: 16 November 2024
Accepted manuscript online: 05 December 2024

PACS:	89.75.-k	(Complex systems)
	89.75.Fb	(Structures and organization in complex systems)
	02.40.-k	(Geometry, differential geometry, and topology)

Fund: Project partially supported by the National Natural Science Foundation of China (Grant Nos. 61672298 and 62373197), the Major Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province, China (Grant No. 2018SJZDI142), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX23_1045).

Corresponding Authors: Yu-Rong Song
E-mail: songyr@njupt.edu.cn

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Hongbo Qu(曲鸿博), Yu-Rong Song(宋玉蓉), Ruqi Li(李汝琦), Min Li(李敏), and Guo-Ping Jiang(蒋国平) Node ranking based on graph curvature and PageRank 2025 Chin. Phys. B 34 028901

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