  In this paper, we study emergent irreducible information in populations of
randomly generated computable systems that are networked and follow a
"Susceptible-Infected-Susceptible" contagion model of imitation of the fittest
neighbor. We show that there is a lower bound for the stationary prevalence (or
average density of "infected" nodes) that triggers an unlimited increase of the
expected local emergent algorithmic complexity (or information) of a node as
the population size grows. We call this phenomenon expected (local) emergent
open-endedness. In addition, we show that static networks with a power-law
degree distribution following the Barab\'asi-Albert model satisfy this lower
bound and, thus, display expected (local) emergent open-endedness.
