Network centrality, social loops, and utility maximization

Abstract

This study examines the effect of social loops on individual effort. Under a situation wherein agents’ effort induces additional efforts to others through a network, an optimum effort corresponds to the subgraph centrality that captures the number of social loops in a network. In contrast to Bonacich centrality, this centrality avoids a problem of divergence and it is based on bounded rational behaviors. We tested this theoretical fact using data for 122 Japanese university sophomores and juniors from 2013 to 2018. Bonacich cenrality had a divergence problem in all cases. On the other hand, students who had a higher subgraph centrality index tended to put forth more efforts in a class after controlling for the individual characteristics. Subgraph centrality had a robust effect even if we added an effect of other centralities, i.e., out-degree, in-degree, betweenness, and closeness centralities. This fact shows that the social loop of communication was critical in the class of university students.