Identifying influential nodes in social networks considering heterogeneous cost

With the rapid growth of online social platforms, the influence spread analysis in social networks has become increasingly important. Identifying influential nodes while considering both Influence Maximization (IM) and Influence Blocking Maximization (IBM) is a crucial issue in this field. In reality, the costs incurred by each user to participate as a seed in the diffusion process can vary significantly, prompting a focus on identifying influential nodes with heterogeneous cost. To address this, we introduce a two-player zero-sum static attack–defense game model considering cost heterogeneity. The attacker aims to maximize influence propagation while the defender aims to minimize it. By leveraging the equilibrium strategy of this game, we redefine the concept of influential nodes from the perspectives of attackers, defenders, and neutral observers. Experiments on scale-free networks and real-world networks demonstrate the significant impact of cost heterogeneity and resource constraints on the equilibrium strategy for both players. Specifically, when both players have equal available resources, the attacker always drops the critical nodes. As cost heterogeneity increases, the defender shifts from prioritizing critical nodes to abandoning them. This study advances the understanding of influential nodes with heterogeneous costs from an attack–defense game perspective and opens up new avenues for future research.