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如何用定量分析的方法识别复杂网络中的关键节点，或者评估某节点相对于其他一个或多个节点的重要程度，是网络科学研究的热点问题。针对节点重要性识别中存在的指标权重主观赋值和全局和局部信息融合不足等问题，本文提出一种基于信息熵赋权的多通道卷积神经网络框架（entropy-based weighted multi-channel convolutional neural networkframework，EMCNN）。该方法构建了一种无参熵权分配模型，通过计算不同节点重要性指标的熵权值，突破了传统方法依赖经验参数的局限性。同时，对全局与局部信息进行解耦重构，构建多通道特征图，并结合卷积神经网络的特征提取能力和注意力机制的关键特征融合能力，实现全局与局部特征的深度融合学习，从而更精准地识别网络节点的重要性。为验证该方法的有效性，本文在9个真实世界网络和3个合成网络上利用SIR模型进行仿真实验，结果表明EMCNN方法有效克服了评估角度的局限性，能在不同传播率下对节点的传播影响力进行有效评估，在相关性及准确性上优于当前主流算法。Identifying key nodes in complex networks or evaluating the relative node importance with respect to others using quantitative methods is a fundamental issue in network science. To address the limitations of existing approaches—namely the subjectivity in assigning weights to importance indicators and the insufficient integration of global and local structural information—this paper proposes an entropy-weighted multi-channel convolutional neural network framework (EMCNN). First, a parameter-free entropy-based weight allocation model is constructed to dynamically assign weights to multiple node importance indicators by computing their entropy values, thereby mitigating the subjectivity inherent in traditional parameter-setting methods and enhancing the objectivity of indicator fusion. Second, global and local structural features are decoupled and reconstructed into separate channels to form multi-channel feature maps, which significantly enhance the representational capacity of the network structure. Third, by leveraging the feature extraction capabilities of convolutional neural networks and the integration power of attention mechanisms, the framework extracts deep representations of nodes from the multi-channel feature maps, while emphasizing key structural information through attention-based weighting, thus enabling more accurate identification and characterization of node importance. To validate the effectiveness of the proposed method, extensive experiments are conducted on nine real-world networks using the SIR spreading model, assessing performance in terms of correlation, accuracy, and robustness. The Kendall correlation coefficient is employed as the primary evaluation metric to measure the consistency between predicted node importance and actual spreading influence. Additionally, experiments are performed on three representative synthetic networks to further test the model’s generalizability. Experimental results demonstrate that EMCNN consistently and effectively evaluates node influence under varying transmission rates, and significantly outperforms mainstream algorithms in both correlation and accuracy. These findings highlight the method’s strong generalization ability and broad applicability in key node identification tasks within complex networks.
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Keywords:
- entropy /
- convolutional neural network /
- node importance
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