  Theoretical computer science plays an important role in the understanding of
social networks and their properties. We can model information rippling
throughout social networks, or the opinions of social media users for example,
using graph theory and Markov chains. In this thesis, we model social networks
as graphs, and consider two such processes:
  1. Nodes talk to other nodes and find middle ground, causing their opinions
to come closer to consensus (the load balancing model)
  2. All nodes take the maximum value of their neighbours in lockstep (the
synchronous maximum model)
  We study the convergence behaviours of each process, such as the eventual
state of the graph, the convergence time and the period. We provide proofs of
the eventual states and periods for each of the above models, and theoretical
bounds for the worst case convergence times. We verify these with experiments,
and explore further questions such as the average case convergence time of
various special classes of graphs, or the convergence times when the model is
altered slightly.
