  In today's world, individuals interact with each other in more complicated
patterns than ever. Some individuals engage through online social networks
(e.g., Facebook, Twitter), while some communicate only through conventional
ways (e.g., face-to-face). Therefore, understanding the dynamics of information
propagation among humans calls for a multi-layer network model where an online
social network is conjoined with a physical network. In this work, we initiate
a study of information diffusion in a clustered multi-layer network model,
where all constituent layers are random networks with high clustering. We
assume that information propagates according to the SIR model and with
different information transmissibility across the networks. We give results for
the conditions, probability, and size of information epidemics, i.e., cases
where information starts from a single individual and reaches a positive
fraction of the population. We show that increasing the level of clustering in
either one of the layers increases the epidemic threshold and decreases the
final epidemic size in the whole system. An interesting finding is that
information with low transmissibility spreads more effectively with a small but
densely connected social network, whereas highly transmissible information
spreads better with the help of a large but loosely connected social network.
