Social graph theory believes that one can gather information on the importance of someone based on a map of their social network. Social network analysts believe that the relationships between people are connected like our highway system. The most popular avenue between two points likely represents the closest connection.
Finding the links between people and the chances of them knowing the same person go back as far as the ancient Greek cultures. The origins of social graph theory are found in a paper written by Leonhard Euler during the mid-1750s. Euler put forth a theorem on the use of bridges in Konigsberg. In the early 20th century psychologists such as Jacob Moreno tried to analyze abnormal behavior through the mapping of normal social interaction and developed social graph theory in the process.
Social analysts use mathematics to chart popularity in one's social network. Someone who regularly keeps in contact with many individuals has many nodes connecting to them. Someone who only talks to a few people, even if those are popular people, has only a few nodes on their social graph, and hence is less "popular". Making a graph usually requires specialized computer software and a great deal of mathematical expertise.
Those who work in the business world sometimes use social graph theory to analyze their social networks. Social graphs can improve networking for finding jobs or connections to important potential clients. Businesses may use social graph theory to target potential talent with ties to their own employees, or use in investigations of corporate spying.
Users of social network websites like Facebook and MySpace make use of social graph theory every day. These websites suggest people you may know through links to your other friends. Websites like Classmates that connect people with long-lost friends also use social graph theory to determine the likelihood that a user knows an individual, taking into account not just geography, but also high closeness probabilities due to organization memberships and and other similar interests on their social "map".