1. A computer-based system for presenting interpersonal relationship analysis, comprising: a matching server system, operatively coupled to a public network, having a database that stores match profile data associated with a plurality of users, wherein the match profile data includes self-identified preferences, wherein the matching server system is configured to: correlate a first user's match profile data with one or more of the plurality of users' match profile data; identify an initial set of potential matches for the first user based on the self-identified preferences; calculate one or more compatibility values for each potential match in the initial set of potential matches and remove each potential match that does not satisfy one or more compatibility scores; after the calculation step, if the number of potential matches does not meet a minimum threshold value, then identify an expanded set of potential matches for the first user based on a relaxed set of self-identified preferences.