This article proposes a mathematical model for quantifying relationships between agents within a network basedon their similarity, dissimilarity, level of friendship, group and activity status of the agent. We propose a set offunctions to facilitate quantifying social dynamics. Our functions cover the comparison of an agent with groupand comparing a group with groups based on their set of attributes. We also propose a model of comparison foragent vs. agent based on their attributes, features and the likelihood of attribute similarity between agents. Themodel employs a method of determining connection probabilities between nodes in order to find hiddenconnections between agents. We build on existing work in the study of social networks.