Opinion dynamics in social networks

We study the problem of opinion dynamics in social networks from a mathematical modelling perspective. As a classic model, the voter model has been extensively studied, especially the bound of its expected time to converge to consensus. However, its twin model, the posting model, has not gained as much attention. The comparison between the performance of these two models on various graphs remains unclear. In our work, we first prove the convergence of the posting model, then we compare the two models’ expected time to reach consensus on regular graphs, star graphs and in the situation where two opinions meet on line graphs. We prove on regular graphs, the two models have the same performance while in two latter cases, the voter model always converges faster. A general framework to simulate the two models’ behavior is also provided. Finally, the simulation results of the two models’ time to reach consensus on line graphs, star graphs, random graphs and real-world social networks are demonstrated.Bachelor of Science in Mathematical Science