Polarization in online social networks has gathered a significant amount of attention in the research community and in the public sphere due to stark disagreements with millions of participants in topics surrounding politics, climate, the economy and other areas where an agreement is required. There are multiple approaches to investigating the scenarios in which polarization occurs and given that polarization is not a new phenomenon but that its virality may be supported by the low cost and latency messaging offered by online social media platforms; an investigation into the intrinsic dynamics of online opinion evolution is presented for complete networks. Extending a model which utilizes the Binary Voter Model (BVM) to examine the effect of the degree of freedom for selecting contacts based upon homophily, simulations show that different opinions are reinforced for a period of time when users have a greater range of choice for association. The facility of discussion threads and groups formed upon common views further delays the rate in which a consensus can form between all members of the network. This can temporarily incubate members from interacting with those who can present an alternative opinion where a voter model would then proceed to produce a homogeneous opinion based upon pairwise interactions.

The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased.