Measuring group leadership in networks based on Shapley value

Abstract

Measuring group leadership in social networks is a nontrivial task from a methodological viewpoint. The development of modern computational methods for evaluating group leadership is rooted in the analysis of network centralities. While computational methods for assessing the centralities of individual (i.e., single) nodes in networks have been well established, the methodological apparatus for computing group centralities has been much less developed. In the research domain of quantitative methods, this situation leads to the search for interdisciplinary solutions in which game theory currently plays a dominant role. This study analyzed two computational methods to measure group leadership in networks. Both are based on the game-theoretical concept of the Shapley value (SV). Based on the illustrative networks, the given research shows and discusses the strengths and weaknesses of the approaches. In short, the key finding of the study is that there is no “free lunch” method to measure group leadership, which means that each specific network requires an individual approach for choosing the most appropriate model.