Optimal networks for dynamical spreading

The inverse problem of finding the optimal network structure for a specific type dynamical process stands out as one most challenging problems in science. Focusing on susceptible-infected-susceptible dynamics annealed networks whose structures are fully characterized by degree distribution, we develop an analytic framework to solve problem. We find that, relatively low or high infection rates, distribution is unique, which consists no more than two distinct nodal degrees. For intermediate multitudinous and can have broader support. also general, heterogeneity decreases with rate. A surprising phenomenon existence value rate any would be generating maximum spreading prevalence. findings provide insights into interplay between processes practical implications.