A multi-feature vital node identification scheme in complex networks

Identifying vital nodes in complex networks constitutes a fundamental challenge with profound implications for optimizing information dissemination dynamics. This critical task finds extensive applications across diverse domains including epidemic containment, public opinion management, traffic regulation, and rumor dissemination. However, existing node centrality metrics face inherent limitations arising from their unilateral emphasis on either local neighborhood features (e.g., degree centrality) or global topological properties (e.g., betweenness centrality), thereby failing to reflect the multi-scale influence of nodes comprehensively. To tackle this critical gap, we propose DEGM (Extended Degree and Information Entropy-based Gravity Model), a novel framework that integrates local non-immediate neighbor characteristics with global structural information for improved vital node identification. First, we introduce the extended degree-based index, which systematically incorporates both first-order and second-order neighborhood information through a decay-weighted aggregation mechanism, thereby enabling more precise quantification of nodes' local influence. Furthermore, we integrate information entropy theory into the gravity formulation to dynamically adjust interaction weights between node pairs, effectively capturing the heterogeneity of global influence propagation. In-depth experimental assessments on nine practical networks demonstrate the superior performance of DEGM against 11 state-of-the-art benchmarks. Notably, quantitative analysis reveals that DEGM exhibits excellent discriminative capability in terms of Kendall's tau coefficient, Jaccard similarity, Monotonicity, and complementary cumulative distribution function (CCDF), significantly outperforming conventional centrality methods.