Question

How do centrality and number of friends relate for students in this small environment?

Analysis–Wrangling

library(tidygraph)
## 
## Attaching package: 'tidygraph'
## The following object is masked from 'package:stats':
## 
##     filter
library(ggraph)
## Loading required package: ggplot2
library(ggplot2)
library(igraph)
## 
## Attaching package: 'igraph'
## The following object is masked from 'package:tidygraph':
## 
##     groups
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union
library(readxl)

peers_b <- read_xlsx("data/peers_b.xlsx")
## New names:
## • `0` -> `0...1`
## • `2` -> `2...2`
## • `0` -> `0...3`
## • `2` -> `2...4`
## • `2` -> `2...5`
## • `2` -> `2...6`
## • `2` -> `2...8`
## • `2` -> `2...9`
## • `0` -> `0...10`
## • `0` -> `0...11`
## • `2` -> `2...12`
## • `0` -> `0...13`
## • `0` -> `0...14`
## • `0` -> `0...15`
## • `0` -> `0...16`
## • `2` -> `2...17`
## • `0` -> `0...18`
## • `0` -> `0...19`
## • `0` -> `0...20`
## • `2` -> `2...21`
## • `0` -> `0...22`
## • `2` -> `2...23`
## • `0` -> `0...24`
## • `2` -> `2...25`
## • `0` -> `0...26`
## • `2` -> `2...27`
peers_matrix <- as.matrix(peers_b)

###change names
peers_network <- as_tbl_graph(peers_matrix, 
                                directed = TRUE)

peers_edges <- peers_network |>
  activate(edges) |>
  as_tibble()



peers_nodes <- peers_network |>
  activate(nodes) |>
  as_tibble()

peers_network <- tbl_graph(edges = peers_edges, # specifies edges
                             nodes = peers_nodes, # specifies nodes
                             directed = TRUE) # specifies directionality
#size
gorder(peers_network)
## [1] 53
gsize(peers_network)
## [1] 190
#centrality
centrality_all <- centr_degree(peers_network, mode = "all")
centrality_out <- centr_degree(peers_network, mode = "out")
centrality_in <- centr_degree(peers_network, mode = "in")

Data Product

## Warning: Using the `size` aesthetic in this geom was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` in the `default_aes` field and elsewhere instead.

Narrative Because of the small size of this network, there is less centrality to the peer groups than there would be if the network was larger. This suggests that in a sufficiently small group, the 80/20 rule–that 20% have 80% of resources–either does not apply or has a limited effect on relationships between people. This implies that small class size is good not only for learning and relationship with the teacher, but it is also good for socialization. Notably, there are no isolates in the graph. It may be that cliques–highly clustered groups of actors–either do not form in this environment, or they are looser in it, where people may know each other better as individuals, and less as stereotypes, like the Popular Kid, the Nerd, the Jock.
It would be interesting, however, to get another cultural group’s middle school class to test these hypotheses. Do more collectivist cultures create more, or fewer, cliques in this small-class environment?