Competitivity groups on social network sites

In this paper a new method to classify the users of an SNS (Social Network Site) into groups is shown. The method is based on the PageRank algorithm. Competitivity groups are sets of nodes that compete among each other to gain PageRank via the personalization vector. Specific features of the SNSs (such as number of friends or activity of the users) can modify the ranking inside each Competitivity group. The concept of Leadership Group is also presented. Some numerical examples are shown. These concepts can also be applied to general complex networks.