Importance of initial conditions in the polarization of complex networks

Currently used models of opinion formation use random initial conditions. In reality, most people in a social network, except for a small fraction of the population, are initially either unaware of, or indifferent to, the disputed issue. To explore the consequences of such specific initial conditions, we study the polarization of social networks when conflicting ideas arise on two different seed nodes and then spread according to a majority rule. Using the configuration model and the stochastic block model as examples, we show that this framework leads to substantially different outcomes than those which employ random initial conditions. Moreover, the empirically observed splits in the karate and the dolphins' networks naturally come out of this paradigm. Our work thus suggests that the existing opinion dynamics models should be reevaluated to incorporate the initial condition dependence.