Popularity and Entropy in Friendship and Enmity Networks in Classrooms

Abstract

Looking for regular statistical trends of relations in schools, we constructed 42 independent weighted directed networks of simultaneous friendship and animosity from surveys we made in the Mexico City Metropolitan area in classrooms with students of different ages and levels by asking them to nominate and order five friends and five foes. However, the data show that older students nominated fewer than the five required five foes. Although each classroom was independent of the others, we found several general trends involving students of different ages and grade levels. In all classrooms, friendship entropy was found to be higher than enmity entropy, indicating that fewer students received enmity links than received friendship nominations. Popular agents exhibited more reciprocal nominations among themselves than less popular agents, and opposite-sex friendships increased with age.

Stability of the personal relationship networks in a longitudinal study of middle school students

“…The different character of enmity and friendship networks has also been recently pointed out in Ref. 18 . Note, however, that this does not mean that learning about enmities is irrelevant, as they have been shown to control the community structure of classes in Ref.…”

“…Even if it is not the main objective of our research, we find it interesting to report on our results on negative relationships, or enmities, a subject that has been largely overlooked in the past to the extent that very few results are available. In fact, in the context of schools we are only aware of the contemporaneous work by Sánchez-Espinosa et al 18 , while in a more general (historical) context we can mention the work of Yose et al 19 . Enmities are very few and highly volatile.…”

Modelling the creation of friends and foes groups in small real social networks

“…Such questions have been tackled in some experimental studies [ 25 , 26 ]. For example, in a previous paper some of us performed a study of friends and foes networks in several Mexico city primary and secondary schools [ 25 , 27 ]. Each student was asked to rank eight friends and foes, although later on only five were used to analyze the data.…”