When analyzing the social web, we see various edges (ties or relationships) connecting the nodes (individuals or organizations). Theoretically the strength of the edge or relationship is categorized as strong or weak. In 1973 paper titled "The strength of weak ties" - http://sociology.stanford.edu/people/mgranovetter/documents/granstrengthweakties.pdf Mark Granovetter lays foundations of importance of strength of ties in micro and macro levels of sociology.
Recently I came across a predictive model developed using Facebook which considers seven dimensions of "tie strength" They are: Intensity, Intimacy, Duration, Reciprocal Services, Structural, Emotional Support and Social Distance.
32 Predictive variables from Facebook interactions have been used along with a survey deriving 5 dependent variables that fits into the predictive model.
The model uses statistical linier method to predict the strength of a relationship in continuous 0 - 1 Scale.
More on - http://social.cs.uiuc.edu/people/gilbert/pub/chi09-tie-gilbert.pdf
I like the methodology used and practical approach towards predictive modelling. More stronger the tie, better influence....