  A model for the spreading of online information or "memes" on multiplex
networks is introduced and analyzed using branching-process methods. The model
generalizes that of [Gleeson et al., Phys.Rev. X., 2016] in two ways. First,
even for a monoplex (single-layer) network, the model is defined for any
specific network defined by its adjacency matrix, instead of being restricted
to an ensemble of random networks. Second, a multiplex version of the model is
introduced to capture the behaviour of users who post information from one
social media platform to another. In both cases the branching process analysis
demonstrates that the dynamical system is, in the limit of low innovation,
poised near a critical point, which is known to lead to heavy-tailed
distributions of meme popularity similar to those observed in empirical data.
