Six-degree gravity centrality for detecting influential nodes in networks

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.