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We study emergent information in populations of randomly generated networkedcomputable systems that follow a Susceptible-Infected-Susceptible contagion (orinfection) model of imitation of the fittest neighbor. These networks have ascale-free degree distribution in the form of a power-law following theBarab\'{a}si-Albert model. We show that there is a lower bound for thestationary prevalence (or average density of infected nodes) that triggers anunlimited increase of the expected emergent algorithmic complexity (orinformation) of a node as the population size grows.

Expected Emergence of Algorithmic Information from a Lower Bound for Stationary Prevalence