I've recently had a New paper out in EPJ Data Science concerning preferential attachment (the 'rich get richer' effect) in social networks.
This is a relatively controversial area, and the aim of the paper was to try to be as systematic / objective as possible. The simplest way to explain our results, suggested by one of two pleasingly constructive reviewers, is that we estimate around 40% of social contacts arise due to the existence of existing social contacts (e.g. your friends introduce you to their friends) rather than from direct social activity. If this figure had been much larger, it would have created an epidemiological paradox - no infectious disease would be controllable.
The main innovation was to use a general finite-state-space Markov chain for the non-preferentially attached links, which generates a mechanistically interpretable phase-type distribution as a way to capture other sources of heterogeneity in contact numbers.
The journal's editor (quite a 'big name' with many followers) was also nice enough to promote the work on social media: