Influence problems on a content-spreading model and graph machine learning

Modeling how information or disease spreads on a network is a major problem in network science. The problem of determining seed nodes that maximize influence is called the influence maximization problem and has been well studied for various models of influence dissemination. The influence computation problem has an even more ambitious goal as it seeks to determine the exact probability of particular nodes getting influenced. H. Z. Brooks et al. [arXiv:2403.01066] introduced a model for the spreading of content on networks inspired by bounded confidence models. We show that this content-spreading model generalizes the independent cascade model and propose various influence computation and influence maximization problems. We discuss centrality measures for identifying influential nodes in the case of trees, which is analytically and computationally tractable. Finally, we train graph neural networks to predict the influence probabilities and propose this as a benchmark task to evaluate the oversquashing problem in graph neural networks.