Well, the term "authority" may be not perfect. The "Best friend" is evaluated as power of symmetric interactions between accounts. The "Fan" means person actively votes and comments the account owner not being voted and commented in return - asymmetrically. The "Authority" is the asymmetric opposition to "Fan". We will be publishing the all math under the hood in couple months in the paper. For the time being, there is a presentation describing the idea of the social environment assessment engine:

and there is a paper on it: http://ieeexplore.ieee.org/document/7587680/