Welcome to the *social network analysis* demo! To complete this, click the green arrows to the right of each code chunk.

1. Loading, Setting Up

In this section, we load packages with the library() function and read data using the read_csv() function.

  • d refers to the data we loaded on teachers’ relations
  • u refers to “user”-level data (e.g., on teachers’ years of experience)
set.seed(0811)

library(tidyverse)
library(tidygraph)
## 
## Attaching package: 'tidygraph'
## The following object is masked from 'package:stats':
## 
##     filter
library(ggraph)
library(here)

d <- read_csv(here('data', 'teacher-network-data-relations.csv'))
## 
## ── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   name = col_character(),
##   most_helpful_1 = col_character(),
##   most_helpful_2 = col_character(),
##   most_helpful_3 = col_character()
## )
## Warning: 1 parsing failure.
## row col  expected    actual                                                                           file
##   4  -- 4 columns 3 columns '/Users/joshuarosenberg/aera-workshop/data/teacher-network-data-relations.csv'
u <- read_csv(here('data', 'teacher-network-data-users.csv'))
## 
## ── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   name = col_character(),
##   years_of_experience = col_double(),
##   subject = col_character()
## )

Your Turn ⤵

Run the following two code chunks to take a glimpse at your data. Below, add a few notes on what you notice and wonder

glimpse(d)
## Rows: 12
## Columns: 4
## $ name           <chr> "Mikayla", "Dylan", "Ilyaas", "Wayne", "Kaitlyn", "Camron", "Melody", "Lakota", "Stephanie", "Jessica", "Faseeha", "Pa…
## $ most_helpful_1 <chr> "Dylan", "Faseeha", "Mikayla", "Melody", "Melody", "Melody", "Wayne", "Camron", "Jessica", "Faseeha", "Kaitlyn", "Step…
## $ most_helpful_2 <chr> NA, NA, "Melody", "Faseeha", NA, "Lakota", "Faseeha", NA, "Patrick", "Melody", "Mikayla", "Jessica"
## $ most_helpful_3 <chr> NA, NA, NA, NA, NA, NA, NA, NA, "Melody", NA, "Melody", NA
glimpse(u)
## Rows: 12
## Columns: 3
## $ name                <chr> "Mikayla", "Dylan", "Ilyaas", "Wayne", "Kaitlyn", "Camron", "Melody", "Lakota", "Stephanie", "Jessica", "Faseeha"…
## $ years_of_experience <dbl> 1, 27, 4, 7, 5, 0, 10, 2, 3, 2, 18, 1
## $ subject             <chr> "Chemistry", "Biology", "Biology", "Biology", "Biology", "Chemistry", "Chemistry", "Chemistry", "Biology", "Biolo…

What do you notice and/or wonder about this data? Add a note or two below!

2. Preparing Data

In this section, we prepare our data to be in edgelist format.

Your Turn ⤵

d_long <- d %>% 
  pivot_longer(most_helpful_1:most_helpful_3, names_to = "nominee") %>% 
  mutate(nominee_rank = str_sub(nominee, start = -1),
         nominee_rank = as.integer(nominee_rank)) %>% 
  select(-nominee) %>% 
  filter(!is.na(value))

d_long
## # A tibble: 22 x 3
##    name    value   nominee_rank
##    <chr>   <chr>          <int>
##  1 Mikayla Dylan              1
##  2 Dylan   Faseeha            1
##  3 Ilyaas  Mikayla            1
##  4 Ilyaas  Melody             2
##  5 Wayne   Melody             1
##  6 Wayne   Faseeha            2
##  7 Kaitlyn Melody             1
##  8 Camron  Melody             1
##  9 Camron  Lakota             2
## 10 Melody  Wayne              1
## # … with 12 more rows

What is different about the edgelist data now? Add one or more observations (you can add additional observations by adding more dashes):

3. Creating a Graph ‘Object’ and Preparing to Visualize the Network

This next step is key in that we use the tbl_graph() function to create a network “object”; if that sounds a bit vague, it should! An “object” refers to a type of data in R. Here, it’s one that is specific to the packages we are using for social network analysis.

Here, we create a network object with only the edgelist.

g <- tbl_graph(edges = d_long)

g
## # A tbl_graph: 12 nodes and 22 edges
## #
## # A directed simple graph with 1 component
## #
## # Node Data: 12 x 1 (active)
##   name   
##   <chr>  
## 1 Mikayla
## 2 Dylan  
## 3 Faseeha
## 4 Ilyaas 
## 5 Melody 
## 6 Wayne  
## # … with 6 more rows
## #
## # Edge Data: 22 x 3
##    from    to nominee_rank
##   <int> <int>        <int>
## 1     1     2            1
## 2     2     3            1
## 3     4     1            1
## # … with 19 more rows

Your Turn ⤵

Let’s create this object again, but also adding nodes information, or the user-level information we also loaded earlier on.

g <- tbl_graph(edges = d_long, nodes = u)

g
## # A tbl_graph: 12 nodes and 22 edges
## #
## # A directed simple graph with 1 component
## #
## # Node Data: 12 x 3 (active)
##   name    years_of_experience subject  
##   <chr>                 <dbl> <chr>    
## 1 Mikayla                   1 Chemistry
## 2 Dylan                    27 Biology  
## 3 Ilyaas                    4 Biology  
## 4 Wayne                     7 Biology  
## 5 Kaitlyn                   5 Biology  
## 6 Camron                    0 Chemistry
## # … with 6 more rows
## #
## # Edge Data: 22 x 3
##    from    to nominee_rank
##   <int> <int>        <int>
## 1     1     2            1
## 2     2    11            1
## 3     3     1            1
## # … with 19 more rows
g <- g %>% 
  mutate(popularity = centrality_degree(mode = 'in')) %>% 
  activate("edges") %>% 
  mutate(nominee_rank = as.factor(nominee_rank))

g
## # A tbl_graph: 12 nodes and 22 edges
## #
## # A directed simple graph with 1 component
## #
## # Edge Data: 22 x 3 (active)
##    from    to nominee_rank
##   <int> <int> <fct>       
## 1     1     2 1           
## 2     2    11 1           
## 3     3     1 1           
## 4     3     7 2           
## 5     4     7 1           
## 6     4    11 2           
## # … with 16 more rows
## #
## # Node Data: 12 x 4
##   name    years_of_experience subject   popularity
##   <chr>                 <dbl> <chr>          <dbl>
## 1 Mikayla                   1 Chemistry          2
## 2 Dylan                    27 Biology            1
## 3 Ilyaas                    4 Biology            0
## # … with 9 more rows

What do you notice about the g network object? How does it appear different from either the edgelist or the user-level data we loaded?

4. Creating and Refining a Network Visualization

Perhaps our question has to do with who is most central (and, possibly, the most influential) within our network.

Let’s start with a simple visualization of our network using geom_edge_fan() and geom_node_point().

ggraph(g, layout = 'kk') + 
  geom_edge_fan() +
  geom_node_point() +
  theme_graph()

We can enhance this visualization in numerous ways, such as by:

  • Sizing the points based on popularity, or in-degree centrality (how many times a person was a nominee)
  • Coloring the points by subject
  • Changing the hue of the edges based upon the order in which one was nominated
ggraph(g, layout = 'kk') + 
  geom_edge_fan(aes(alpha = nominee_rank), 
                arrow = arrow(length = unit(4, 'mm')),
                start_cap = circle(6, 'mm'),
                end_cap = circle(6, 'mm')) + 
  geom_node_point(aes(size = popularity, color = subject)) +
  theme_graph()

We might wish instead to size the points by years of experience, as we do below.

ggraph(g, layout = 'kk') + 
  geom_edge_fan(aes(alpha = nominee_rank), 
                arrow = arrow(length = unit(4, 'mm')),
                start_cap = circle(6, 'mm'),
                end_cap = circle(6, 'mm')) + 
  geom_node_point(aes(size = years_of_experience, color = subject)) +
  theme_graph()

We can use names (if anonymized or otherwise ethically appropriate for our analysis), as below.

ggraph(g, layout = 'kk') + 
  geom_edge_fan(aes(alpha = nominee_rank), 
                arrow = arrow(length = unit(4, 'mm')),
                start_cap = circle(6, 'mm'),
                end_cap = circle(6, 'mm')) + 
  geom_node_label(aes(label = name, size = popularity)) +
  theme_graph()

Lastly, we can identify sub-groups within our network and use color to indicate which individuals are a part of which sub-groups, as below.

g %>%
  activate(nodes) %>%
  mutate(group = group_spinglass()) %>% 
  ggraph(layout = 'kk') + 
  geom_edge_fan(aes(alpha = nominee_rank), 
                arrow = arrow(length = unit(4, 'mm')),
                start_cap = circle(6, 'mm'),
                end_cap = circle(6, 'mm')) + 
  geom_node_label(aes(label = name, size = popularity, color = as.factor(group))) +
  theme_graph() +
  scale_color_discrete("Group", type = "qual")

Your Turn ⤵

Which visualization is most helpful for understanding who may be influential in the network? Why?

5. Calculating Descriptive Statistics

Finally, we can calculate a range of network statistics, as below.

g <- g %>% 
  activate("nodes") %>% 
  rename(in_degree_centrality = popularity) %>% 
  mutate(out_degree = centrality_degree(mode = 'out')) %>% 
  mutate(betweenness_centrality = centrality_betweenness()) %>% 
  mutate(centrality_eigen = centrality_eigen())

g %>% 
  as_tibble() %>% 
  skimr::skim()
Data summary
Name Piped data
Number of rows 12
Number of columns 7
_______________________
Column type frequency:
character 2
numeric 5
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
name 0 1 5 9 0 12 0
subject 0 1 7 9 0 2 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
years_of_experience 0 1 6.67 8.14 0.00 1.75 3.50 7.75 27 ▇▂▁▁▁
in_degree_centrality 0 1 1.83 1.90 0.00 1.00 1.00 2.00 7 ▇▂▁▁▁
out_degree 0 1 1.83 0.72 1.00 1.00 2.00 2.00 3 ▅▁▇▁▂
betweenness_centrality 0 1 7.00 10.44 0.00 0.00 2.50 7.75 31 ▇▂▁▁▂
centrality_eigen 0 1 0.44 0.27 0.11 0.26 0.34 0.56 1 ▇▅▃▁▃

We could also group our data by either years of experience or subject to begin to understand differences in centrality (and, potentially, influence), as below.

g %>% 
  as_tibble() %>% 
  group_by(subject) %>% 
  select(-name) %>% 
  summarize(mean_in_degree_centrality = mean(in_degree_centrality),
            sd_in_degree_centrality = sd(in_degree_centrality))
## # A tibble: 2 x 3
##   subject   mean_in_degree_centrality sd_in_degree_centrality
##   <chr>                         <dbl>                   <dbl>
## 1 Biology                        1.43                    1.27
## 2 Chemistry                      2.4                     2.61
g %>% 
  as_tibble() %>% 
  mutate(high_experience = if_else(years_of_experience > 5, 1, 0)) %>% 
  group_by(high_experience) %>% 
  summarize(mean_in_degree_centrality = mean(in_degree_centrality),
            sd_in_degree_centrality = sd(in_degree_centrality))
## # A tibble: 2 x 3
##   high_experience mean_in_degree_centrality sd_in_degree_centrality
##             <dbl>                     <dbl>                   <dbl>
## 1               0                      1.12                   0.641
## 2               1                      3.25                   2.87

Your Turn ⤵

Based on the descriptive statistics, what can we say is associated with an individual being more (or less) central in the network?