Analytical Modeling of Social Network Growth Using Multilayer Network Projection

In this study, we present a new network model to address the question of how social networks such as groups in social websites, networks of social events, online video game groups evolve in time. A common feature of all these networks is that first, new users attach to an existing group (clique), and second, the decision of new network users is greatly influenced by already-joined users. In our model, new user joins the underlying network from a parallel network layer as the consequence of influence of underlying network users on the ones from other networks. This influence could be any type of relationship exterior to the underlying network layer such as friendship. For the new network model design, we utilize the concepts behind: 1. Growing network model presented by Barabási–Albert (BA), 2. Social influence-driven contagion model and 3. Multiplex network model. The way we treat this challenging phenomena is by multilayer projection, i.e. friends of each actual user that exist in other social network layers are projected as virtual users onto the underlying network layer. At each time step, each virtual user might become actual user based on a proposed Social influence-driven contagion method.