基于社区发现和LDD的复杂网络节点重要性度量

Measuring Node Importance in Complex Networks Based on Community Detection and LDD

摘要: 复杂网络关键节点识别对舆情传播控制、疾病防控和系统稳定性维护等具有重要意义。针对K-shell分解划分粗粒度、全局最小度分解LDD忽略社区结构而难以刻画局部核心节点的问题，本文提出基于社区发现和最小度分解的节点重要性度量方法CD-LDD+。该方法采用谱平分法划分社区诱导子图，在社区内部执行LDD分解，获得节点局部剥离层级；再引入社区内标准化层级得分和平滑因子，融合全局一阶邻居结构贡献，构建综合评价指标。以Zachary’s Karate Club网络为对象，与度中心性、K-shell和Global LDD对比，并通过单调性指数、Kendall秩相关系数和SIR传播模型验证。实验结果表明，CD-LDD+可减少排序并列，提高节点区分度，并增强节点重要性排序与传播影响力的一致性。

Abstract: Identifying key nodes in complex networks is of great significance for public opinion propagation control, disease prevention and control, and maintaining system stability. To address the limitations of K-shell decomposition, which suffers from coarse-grained partitioning, and the global minimum-degree decomposition (LDD), which overlooks community structures and thus fails to characterize local core nodes, this paper proposes a node importance measurement method based on community detection and minimum-degree decomposition, named CD-LDD+. The method first employs the spectral bisection method to partition community-induced subgraphs, then performs LDD decomposition within each community to obtain local peeling hierarchies. Furthermore, it introduces intra-community normalized layer scores and a smoothing factor, and integrates the structural contributions of global first-order neighbors to construct a comprehensive evaluation index. Using Zachary’s Karate Club network as a test case, the proposed method is compared with degree centrality, K-shell, and Global LDD, and is validated through the monotonicity index, Kendall rank correlation coefficient, and the SIR propagation model. Experimental results demonstrate that CD-LDD+ can reduce ranking ties, improve node discrimination, and enhance the consistency between node importance ranking and propagation influence.