Exploring the optimal network topology for spreading dynamics

Complex networks are a useful method to model many real-world systems from society to biology. Spreading dynamics of complex networks has attracted more and more attention and is currently an area of intense interest. In this study, by applying a perturbation approach to an individual-based susceptible–infected–susceptible (SIS) model, we derive an estimation of the incremental spreading prevalence after the network adds a single link and then propose a strategy to find the corresponding optimal link to promote spreading prevalence. Through theoretical analysis, we notice that the proposed strategy can be approximately interpreted by the eigenvector centrality when the infection probability is near the spreading critical point. By comparing the incremental prevalence of several typical synthetic and real networks, we find that the proposed strategy is superior to other methods such as linking nodes with the highest degree and eigenvector centrality. Moreover, the optimal link structure has degree mixing characteristics distinguishable for different spreading parameters. We further demonstrate this finding based on the degree-preserving network configuration model with different rich-club and assortativity coefficients.