Critical exponents of master-node network model

The dynamics of competing opinions in social network plays an important role in society, with many applications in diverse social contexts such as consensus, election, morality, and so on. Here, we study a model of interacting agents connected in networks in order to analyze their decision stochastic process. We consider a first-neighbor interaction between agents in a one-dimensional network with the shape of ring topology. Moreover, some agents are also connected to a hub, or master node, who has preferential choice or bias. Such connections are quenched. As the main results, we observed a continuous nonequilibrium phase transition to an absorbing state as a function of control parameters. By using the finite-size scaling method we analyzed the static and dynamic critical exponents to show that this model probably cannot match any universality class already known.