A state transition-based method for influence evaluation in networks

The influence maximization (IM) problem has been a persistent challenge in network science. However, how to explore higher-order networks, such as weighted hypergraphs, from multiple perspectives and fully leverage the structural properties of higher-order interactions remains an unresolved issue. In this study, we investigate the IM problem in weighted hypergraphs by introducing a novel dynamics model called adaptive dissemination (AD). Firstly, a state transition-based method is innovatively proposed for accurately evaluating the expected influence of multi-hop area (EIMA). This method dynamically transitions node states to measure influence within an arbitrary hop range, providing a universal framework for influence analysis in various networks and dissemination models. Secondly, we further develop three search strategies under the EIMA metric to efficiently solve the seed set in influence maximization. Thirdly, extensive experiments are conducted on real-world datasets, and our algorithms are compared with several state-of-the-art baseline algorithms. Additionally, the comprehensive visual analysis and statistical tests demonstrate that the proposed algorithms significantly outperform existing baselines in overall performance. Finally, we explore the similarity between different seed sets and the impact of varying dissemination parameters, thoroughly validating the efficiency and stability of our algorithms. In summary, this study holds significant value for realistic scenarios such as digital marketing, public opinion monitoring, and epidemic intervention, providing theoretical support and practical guidance for identifying key nodes and optimizing resource allocation.