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Popularity and Entropy in Friendship and Enmity Networks in Classrooms - PubMed

  • ️Sun Jan 01 2023

Popularity and Entropy in Friendship and Enmity Networks in Classrooms

Diego B Sánchez-Espinosa et al. Entropy (Basel). 2023.

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.

Keywords: enmity networks; friendship networks; local entropy; popularity; weighted networks.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1

This bar plot displays the total number of students and teachers in each classroom, categorized by genre and ordered from the lowest average age starting from the left.

Figure 2
Figure 2

Example networks with only friendship and only enmity shown separately for the same classroom. The thickness corresponds to the intensity of the relationship, with thinner lines indicating intensity 1 and thicker lines indicating intensity 5. (a) Subnetwork with only friendship ties; (b) Subnetwork with only enmity ties.

Figure 3
Figure 3

Same as Figure 2, except showing subnetworks with only reciprocal links. The thickness corresponds to the intensity of the relationship, with thinner lines indicating intensity 1 and thicker lines indicating intensity 5. (a) Subnetwork with reciprocal friendship ties; (b) Subnetwork with reciprocal enmity ties.

Figure 4
Figure 4

(Left panel): classroom networks with 36 nodes (students) indicated by gender, average age 13.74 years old. Node colors correspond to the total strength, with red indicating negative total strength (indicative of enmity) and white indicating positive total strength (indicative of friendship). (Right panel): corresponding scatterplot of received individual friendship and enmity entropy values. Only those members with nonzero receiving input links for both friendship and enmity are shown.

Figure 5
Figure 5

Average input entropy values for friendly relationships (green) and enmity relationships (red) of 42 classrooms networks, sorted in ascending order from left to right according to average age.

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