Cross-layers cascade in multiplex networks

The study of information cascade in multiplex networks, where agents are connected by using multiple linking types, has received increasing attention. Compared with the cascade in simplex networks, a noticeable characteristic of the cascade in multiplex networks is that information may be spread between multiple layers. In this study, we focus on the cross-layers cascade, which helps clarify two opposing opinions about the information cascade in multiplex networks: multiplexity can speed up or slow down information cascade. The linear threshold model is generalized into multiplex networks as conjoint agents become active, if the influences of active neighbors in any layer reach a predefined threshold. The preconditions and reasons for the slow-down and speed-up phenomena are discussed using four representative case studies and theoretical analyses. Next, analytical results are validated by using extensive simulations in which the multiplex networks are generated by random, small-world and scale-free network models. It is found that the slow-down phenomenon emerges due to the obstruction of cross-layers cascade which connects the distributed shortest path in multiple layers and the inhibitory effect of negative influence. Conversely, extra short paths or rapid spreading in one additional layer can facilitate the cascade process in existing networks, respectively. Extensive simulations also show that multiplex networks consisting of different network models are more competent for the cascade process compared with multiplex networks generated by a single network model. In conclusion, the concept of cross-layers cascade may elucidate the additional study of information spreading in multiplex networks.