Modeling opinion dynamics in a social network using Markov random field

We propose a Markov Random Field (MRF) based opinion model for social networks that allows for negative, neutral and positive opinions with different magnitudes at discrete levels. The opinion held by a node depends both on its intrinsic behavior (which is external to the network), and its neighbors. This model may be useful in studying firms competing for market share, political parties competing in elections, etc. We characterize the steady state of the proposed model using two methods. The first simulates the above MRF based opinion model using periodic Gibbs sampling, while the second numerically computes the steady state probability distribution of the system using fixed point iteration technique. We present numerical results and insights on synthetic as well as real social networks. In the experiments, we find that the system reaches steady state in a short time. The advantage held by a less popular opinion in the initial stages of system evolution is quickly lost to the more popular opinion in the system. Also, heavy tailed networks require larger safety margins in applications where we need to guarantee some minimum level of prevalence of a desired opinion.