The paper itself is interesting, of course. Conductance often appears in bounds on mixing times for Markov chains, but the rumor spreading problem is a bit different than the consensus problems that I have studied in the past. A nice quote from the introduction:
Our long term goal is to characterize a set of necessary and/or suffcient conditions for rumour spreading to be fast in a given network. In this work, we provide a very general suffcient condition — high conductance. Our main motivation comes from the study of social networks. Loosely stated, we are looking after a theorem of the form “Rumour spreading is fast in social networks”. Our result is a good step in this direction because there are reasons to believe that social networks have high conductance.