Roles of shortcuts in the diffusion process over hierarchical networks

Tree-type hierarchical organizations are ubiquitous in human relationships, especially in social networks connected by a variety of information-rich ties among a population of individuals. In this paper, we consider a continuous-state susceptible-infected-susceptible (SIS) model, where individuals possess fractions of the information and update them by exchanging messages with their neighbors in the vicinity. We find that the spreading criticality condition for information diffusion depends on the largest eigenvalue of a topology-related tridiagonal matrix. Furthermore, based on the eigenvalue perturbation analysis we propose an importance centrality of shortcuts that are added to the hierarchical backbone of the network. Our approach has potential for improving the communicability of tree-type social networks.