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<p>Complex networks modeling social, biological, and technological systems require precise detection of key nodes to understand dynamics and enhance resilience. Key node detection (KND) is a critical fundamental issue, whose purpose is to identify the collection of important nodes and maximize their influence in the entire network. Existing methods often trade-off accuracy for computational efficiency. For large-scale networks, KND requires efficient and time-sensitive computation, making scalable methods important for high-performance graph analysis. In this work, we explicate the KND problem and propose the Composite Entropy-Based Gravity Model (CEGM) that integrates four innovations: (1) standardized centrality metrics merging degree centrality and <i>k</i>-shell indices, (2) information entropy to quantify local structural richness, (3) exponential enhancement terms for high-degree nodes, and (4) <i>k</i>-shell-based structural coefficient weight reflecting topological affinity. The CEGM value is computed via a modified gravity formula incorporating these components. Validated across nine distinct networks, experimental results show CEGM outperforms twelve benchmark methods in terms of Kendall’s correlation coefficient, Jaccard similarity, Error function, as well as Monotonicity index. This framework advances critical node detection by balancing accuracy and efficiency, and future work will further extend CEGM to more complex network scenarios, such as weighted, directed, temporal, and multilayer networks.</p>

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Composite entropy-based gravity model for key node detection in complex networks

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Cuican Wang,
  • Jiafei Liu,
  • Jingli Wu

摘要

Complex networks modeling social, biological, and technological systems require precise detection of key nodes to understand dynamics and enhance resilience. Key node detection (KND) is a critical fundamental issue, whose purpose is to identify the collection of important nodes and maximize their influence in the entire network. Existing methods often trade-off accuracy for computational efficiency. For large-scale networks, KND requires efficient and time-sensitive computation, making scalable methods important for high-performance graph analysis. In this work, we explicate the KND problem and propose the Composite Entropy-Based Gravity Model (CEGM) that integrates four innovations: (1) standardized centrality metrics merging degree centrality and k-shell indices, (2) information entropy to quantify local structural richness, (3) exponential enhancement terms for high-degree nodes, and (4) k-shell-based structural coefficient weight reflecting topological affinity. The CEGM value is computed via a modified gravity formula incorporating these components. Validated across nine distinct networks, experimental results show CEGM outperforms twelve benchmark methods in terms of Kendall’s correlation coefficient, Jaccard similarity, Error function, as well as Monotonicity index. This framework advances critical node detection by balancing accuracy and efficiency, and future work will further extend CEGM to more complex network scenarios, such as weighted, directed, temporal, and multilayer networks.