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, each defined as a specific numerical value, and a previous history of matches and satisfaction rate, wherein the matching server system is configured to: compare the self-identified preferences of a first user's match profile data with the match profile data of one or more other users; calculate a mathematical distance between the self-identified preferences of the first user and the match profile data of the one or more other users, wherein the mathematical distance is a quantitative difference between the numerical values of the first user's self-identified preferences and corresponding numerical values of the match profile data of the one or more other users; identify an initial set of potential matches for the first user based on a maximum distance between the self-identified preferences of the first user and the match profile data of the one or more other users; calculate one or more compatibility values for each potential match in the initial set of potential matches, wherein the one or more compatibility values are calculated based, at least in part, on the previous history of matches and satisfaction rate of each match in the initial set and the first user, and remove each potential match that does not satisfy one or more minimum compatibility values; 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 by increasing the maximum distance.