Identifying influential spreaders in reversible process

Identifying nodes with strong spreading capability is essential to control the spreading dynamics in many real-world scenarios, such as to direct the diffusion of public opinion, promote the adoption of new products and control the spreading of disease in social networks. Previous researches focused on the irreversible propagation process, such as the independent cascade model and the threshold model, which can be categorized into the Susceptible-Infected-Recovered (SIR) model type. The other type is the reversible propagation process with steady state such as the Susceptible-Infected-Susceptible (SIS) model, where the question of identifying important nodes has not received enough attention. In this paper, we study the problem of identifying vital nodes in the SIS spreading process in complex networks. We articulate a single-node control model to evaluate the influence of nodes in the reversible spreading system. By considering network structural and reversible spreading characteristics, we propose a new measure to quantify the node influence based on its neighbors’ centrality and infection risk. By applying the commonly used centralities such as degree and coreness, this new measure can identify the most influential spreaders more accurately than the benchmark centralities. The proposed single-node control model and ranking method open up a new idea in identifying influential spreaders and validate the necessity of introducing the dynamical state in the reversible systems.