Identifying influential spreaders in complex networks is a critical challenge in network science, with broad applications in disease control, information dissemination, and influence analysis in social networks. The gravity model, a distinctive approach for identifying influential spreaders, has attracted significant attention due to its ability to integrate node influence and the distance between nodes. However, the law of gravity is symmetric, whereas the influence between different nodes is asymmetric. Existing gravity model-based methods commonly rely on the topological distance as a metric to measure the distance between nodes. Such reliance neglects the strength or frequency of connections between nodes, resulting in symmetric influence values between node pairs, which ultimately leads to an inaccurate assessment of node influence. Moreover, these methods often overlook cycle structures within networks, which provide redundant pathways for nodes and contribute significantly to the overall connectivity and stability of the network. In this paper, we propose a hybrid method called HGC, which integrates the gravity model with effective distance and incorporates cycle structure to address the issues above. Effective distance, derived from probabilities, measures the distance between a source node and others by considering its connectivity, providing a more accurate reflection of actual relationships between nodes. To evaluate the accuracy and effectiveness of the proposed method, we conducted several experiments on eight real-world networks based on the Susceptible-Infected-Recovered model. The results demonstrate that HGC outperforms seven compared methods in accurately identifying influential nodes.

翻译：识别复杂网络中的影响力传播者是网络科学中的一个关键挑战，在疾病控制、信息传播以及社交网络影响力分析等领域具有广泛应用。引力模型作为一种识别影响力传播者的独特方法，因其能够整合节点影响力与节点间距离而受到广泛关注。然而，万有引力定律是对称的，而不同节点间的影响力却具有不对称性。现有的基于引力模型的方法通常依赖拓扑距离作为度量节点间距离的指标。这种依赖忽略了节点间连接的强度或频率，导致节点对之间的影响力值对称，最终造成节点影响力评估不准确。此外，这些方法往往忽视了网络中的环结构，这些结构为节点提供了冗余路径，并对网络的整体连通性和稳定性有重要贡献。本文提出了一种名为HGC的混合方法，该方法将引力模型与有效距离相结合，并融入了环结构以解决上述问题。有效距离基于概率推导，通过考虑源节点的连通性来度量其与其他节点之间的距离，从而更准确地反映节点间的实际关系。为了评估所提方法的准确性和有效性，我们基于易感-感染-恢复模型在八个真实世界网络上进行了多项实验。结果表明，HGC在准确识别影响力节点方面优于七种对比方法。