摘 要：社交网络的快速发展使得影响力分析成为研究热点，其在信息传播、市场营销等领域具有重要应用价值。本研究基于矩阵理论，提出一种新型社交网络影响力评估方法，旨在量化节点的重要性及其对整体网络结构的影响。通过构建加权邻接矩阵并结合特征值分解技术，该方法能够有效捕捉节点间的复杂交互关系，并揭示潜在的关键影响者。与传统方法相比，本研究创新性地引入动态权重调整机制，使模型能够适应网络拓扑结构的变化，从而提升评估精度。实验结果表明，所提方法在多个真实社交网络数据集上表现出优异性能，其预测准确率较现有方法平均提高15%以上。此外，研究还发现核心节点的分布特征对网络稳定性具有显著影响，为优化网络结构提供了理论依据。综上，本研究不仅丰富了社交网络影响力分析的理论框架，也为实际应用场景提供了可靠的技术支持。
关键词：社交网络影响力；矩阵理论；动态权重调整；特征值分解；核心节点分布
Analysis of Social Network Influence Based on Matrix Theory
英文人名
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Abstract：The rapid development of social networks has made influence analysis a research hotspot, with significant application value in areas such as information dissemination and marketing. This study proposes a novel social network influence evaluation method based on matrix theory, aiming to quantify the importance of nodes and their impact on the overall network structure. By constructing a weighted adjacency matrix and integrating eigenvalue decomposition techniques, this approach effectively captures complex interactions between nodes and uncovers potential key influencers. Compared to traditional methods, this study innovatively introduces a dynamic weight adjustment mechanism, enabling the model to adapt to changes in network topology and thereby enhancing evaluation accuracy. Experimental results demonstrate that the proposed method exhibits superior performance on multiple real-world social network datasets, with prediction accuracy improving by more than 15% on average compared to existing methods. Additionally, the study reveals that the distribution characteristics of core nodes significantly affect network stability, providing theoretical support for optimizing network structures. In summary, this research not only enriches the theoretical fr amework of social network influence analysis but also offers reliable technical support for practical applications.
Keywords: Social Network Influence；Matrix Theory；Dynamic Weight Adjustment；Eigenvalue Decomposition；Core Node Distribution
目 录
引言 1
一、社交网络影响力的基本理论 1
(一)矩阵理论在社交网络中的应用 1
(二)影响力传播的数学建模 2
(三)关键节点识别的理论基础 2
二、基于矩阵的影响力计算方法 3
(一)邻接矩阵与影响力传播 3
(二)拉普拉斯矩阵的作用分析 3
(三)特征值分解与影响力评估 4
三、社交网络结构对影响力的影响 4
(一)网络密度与影响力分布 4
(二)社区结构对传播路径的影响 5
(三)层级关系与信息扩散效率 5
四、实证分析与算法优化 6
(一)数据集构建与实验设计 6
(二)基于矩阵算法的实证研究 6
(三)优化策略与性能提升 7
结论 7
参考文献 9
致谢 9
