A social communication model based on simplicial complexes

Networks offer a powerful language with which to describe and study pairwise interaction. However, in many contexts, these rich collective phenomena require a higher-order approach to encode dynamical processes — for example in idea integration and information transmission (co-publication is a particularly familiar example). Here we introduce a novel framework for social communication by reshaping the networked system to be a simplicial complex, where the communication involves the interaction not only of individual nodes but also among cliques to which they belong. Simplicial complexes extend the network-based pairwise relationship to multiagent interaction. Assuming that the same individual in different cliques may play different roles, a threshold is designed and combined with the node state to determine the clique state. We employ the discrete microscopic Markov chain approach to model the simplex-based social communication and then obtain the underlying critical condition for information outbreaks. Moreover, we perform extensive numerical analysis of the proposed simplicial complex-based communication model and compare its performance with Monte Carlo simulation.