Six-degree gravity centrality for detecting influential nodes in networks

doi:10.1088/1674-1056/adec62

Abstract Identifying critical nodes is a pivotal research topic in network science, yet the efficient and accurate detection of highly influential nodes remains a challenge. Existing centrality measures predominantly rely on local or global topological structures, often overlooking indirect connections and their interaction strengths. This leads to imprecise assessments of node importance, limiting practical applications. To address this, we propose a novel node centrality measure, termed six-degree gravity centrality (SDGC), grounded in the six degrees of separation theory, for the precise identification of influential nodes in networks. Specifically, we introduce a set of node influence parameters—node mass, dynamic interaction distance, and attraction coefficient—to enhance the gravity model. Node mass is calculated by integrating K-shell and closeness centrality measures. The dynamic interaction distance, informed by the six-degrees of separation theory, is determined through path searches within six hops between node pairs. The attraction coefficient is derived from the difference in K-shell values between nodes. By integrating these parameters, we develop an improved gravity model to quantify node influence. Experiments conducted on nine real-world networks demonstrate that SDGC significantly outperforms nine existing classical and state-of-the-art methods in identifying the influential nodes.

Keywords: gravity model influential nodes six degrees of separation semi-local information

Received: 01 June 2025
Revised: 04 July 2025
Accepted manuscript online: 07 July 2025

PACS:

89.75.Hc

(Networks and genealogical trees)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 62173065), the Natural Science Foundation of Beijing (Grant No. 4242040), the Intelligent Policing and National Security Risk Management Laboratory Open Topics for the year 2025 (Grant No. ZHKFYB2503), and the Intelligent Policing and National Security Risk Management Laboratory Open Topics for the year 2024 (Grant No. ZHKFZD2401).

Corresponding Authors: Jianbo Wang, Xiao-Ke Xu
E-mail: jianbow2021@gmail.com;xuxiaoke@foxmail.com

Cite this article:

Jianbo Wang(王建波), Bohang Lin(林渤杭), Zhanwei Du(杜占玮), Ping Li(李平), and Xiao-Ke Xu(许小可) Six-degree gravity centrality for detecting influential nodes in networks 2025 Chin. Phys. B 34 088902

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