On the Submodularity of Diffusion Models: Equivalent Conditions and Applications

The diffusion model has been a crucial component in studies about social networks. Many studies, especially these about influence maximization concern the proof of the submodularity of particular diffusion models. Such proofs have been model-dependent and are somewhat ad hoc. In this paper, we prove a theorem that provides a necessary and sufficient condition for a diffusion model to be submodular. This theorem can be used to justify the submodularity of an arbitrary diffusion model. We also apply this theorem to build a projection operator that maps an arbitrary diffusion model into a submodular one. Moreover, we use the established theorem to propose a diffusion model of multiple heterogeneous pieces of information that partially features submodularity.