I would be interested to see how PageRank could be applied to people rather than web pages. Some thoughts:
PageRank type mechanism for employee performance reviews
Every person in an organisation is asked to rank their satisfaction of their interaction with every other person of the organisation they've interacted with (with N/As against those they haven't interacted with). In itself, such data would be useful, but it would also be possible to recursively analyse, to take into account the satisfaction scores of the incoming satisfaction scores for a person. This would tend to reduce the influence of a small group trying to game the system by giving each other high satisfaction scores.
Other data could also be used to weight the satisfaction scores, such as employee grade. One might envision that employees who satisfy higher grade employees more would be well rewarded.
A spin-off benefit of such an approach to employee performance review is that it gives data on the connections between all employees, potentially identifying key "connector" people, and also showing those that perhaps need to work on their communication and networking skills.
Facebook and other social networks
There have been published articles on the most popular person on Facebook, but these take gross followers scores. A recursive analysis would be informative: who has the most popular friends?