During the summer of 2013—2014 I studied the statistical properties of complex networks while on an Australian Mathematical Sciences Institute (AMSI) summer vacation scholarship. The goal of this project was to understand what makes real world complex networks special. We used a Markov Chain Monte Carlo method (where we perturbed the edge structure of the network) to explore the space of complex networks with the same degree distribution as some real world networks.
A brief blog post that was published just after the completion of the project can be found here (in hindsight it could have done with a quick proof read!).