My Best Current Friend in a Social Network

Due to its popularity, social networks (SNs) have been subject to different analyses. A research field in this area is the identification of several types of users and groups. To make the identification process easier, a SN is usually represented through a graph. Usual tools to analyze a graph are the centrality measures, which identify the most important vertices. One of these measures is the PageRank (a measure originally designed to classify web pages). Informally, in the context of a SN, the PageRank of a user i represents the probability that another user of the SN is seeing the page of i after a considerable time of navigation in the SN. In this paper, we define a new type of user in a SN: the best current friend. Informally, the idea is to identify, among the friends of a user i, who is the friend k that would generate the highest decrease in the PageRank of i if k stops being his/her friend. This may be useful to identify the users/customers whose friendship/relationship should be a priority to keep