Identifying key players in networks of social interactions

Abstract

Purpose: Identifying key players in a group of students using the mathematical methods and models. Discussion: the article contains the sociometric procedure and the results of the calculations. There are various measures of centrality, which allows to identify the most important vertices in the graph. It is shown that the individual sociometric indices are identical to the one of the measures of centrality. Results: It is shown that the leadership depends on the situation and the group`s goals and objectives. It has been identified the various leaders in three situations (learning, solving business tasks, joint leisure activities), depending on the possible goals and objectives that define the criteria of leadership (the presence of a large number of contacts, the control connections between the defined positions, the proximity to other nodes or just their availability, the relationships with the powerful peaks).