Influence maximization based on simplicial contagion models

In recent years, the exploration of node centrality has received significant attention and extensive investigation, primarily fuelled by its applications in diverse domains such as product recommendations, opinion propagation, disease spread, and other scenarios requiring the maximization of node influence. Despite various perspectives emphasizing the indispensability of higher-order networks, research specifically delving into node centrality within the realm of hypergraphs has been relatively constrained. This study delves into the Simplicial Contagion Model (SCM) within the context of influence maximization (IM), specifically utilizing the susceptible-infected-recovered (SIR) model for illustration. To address the optimization challenge associated with IM on SCM, we present a comprehensive theoretical framework grounded in the message passing process. Additionally, we conduct a thorough stability analysis of equilibrium solutions within the self-consistent equations. Furthermore, we introduce a metric called collective influence and propose an adaptive algorithm, known as the Collective Influence Adaptive (CIA), to identify influential propagators in the spreading process. Notably, our algorithm distinguishes itself by prioritizing collective influence over individual influence, resulting in demonstrably superior performance, a characteristic substantiated by a comprehensive array of experiments.