12 — Relational Data (2)

Kieran Healy

January 23, 2024

Relational Data (pt 2)

Load the packages, as always

library(here)      # manage file paths
library(socviz)    # data and some useful functions
library(tidyverse) # your friend and mine

Specialty packages

library(tidygraph) # tidy management of relational data
library(ggraph)   # geoms for drawing graphs

#remotes::install_github("kjhealy/kjhnet")
library(kjhnet)   # some network datasets

The Iliad

• Who is the most central figure in The Iliad?
• We’ll use a “dataset” from The Iliad to explore some ideas about ways of measuring centrality and how they express different concepts of social status.
• Thanks to Gabriel Rossman (UCLA) for the data and the topic idea. This lecture follows his exposition.

Degree centrality

il_tidy

# A tbl_graph: 311 nodes and 292 edges
#
# A directed multigraph with 23 components
#
# Node Data: 311 × 3 (active)
      id name            affil
   <int> <chr>           <chr>
 1     1 Antilochus      A    
 2     2 Agenor          T    
 3     3 Telamonian Ajax A    
 4     4 Antiphus        T    
 5     5 Odysseus        A    
 6     6 Peirous         T    
 7     7 ThoasAndraemon  A    
 8     8 Diomedes        A    
 9     9 Agamemnon       A    
10    10 Idomeneus       A    
# ℹ 301 more rows
#
# Edge Data: 292 × 3
   from    to act  
  <int> <int> <chr>
1     1    41 kills
2     2    42 kills
3     3    43 kills
# ℹ 289 more rows

Degree centrality

out <- il_tidy |>
  activate(nodes) |>
  mutate(centrality = centrality_degree()) |>
  as_tibble() |>
  ggplot(mapping = aes(x = centrality)) +
  geom_histogram() +
  labs(x = "Count of Victories", y = "Count of Warriors ") +
  theme_minimal() +
  theme(legend.position = "top")

print(out)

Degree Centrality (with affiliation)

out <- il_tidy |>
  activate(nodes) |>
  mutate(centrality = centrality_degree()) |>
  as_tibble() |>
  arrange(desc(centrality)) |>
  top_n(10, wt = centrality) |>
  ggplot(mapping = aes(x = centrality,
                       y = reorder(name, centrality),
                       color = affil)) +
  geom_point(size = 3) +
  labs(x = "Centrality", y = NULL, color = "Side") +
  theme_minimal() +
  theme(legend.position = "top")

print(out)

Graph representation

out <- il_tidy |>
  activate(nodes) |>
  ggraph(layout = "fr") +
  geom_edge_link(color = "gray80") +
  geom_node_point(aes(color = affil)) +
  scale_color_manual(values = c("blue", "red"), 
                     labels = c("Athenian", "Trojan")) +
  guides(color = guide_legend(title = "Side")) +
  labs(title = "Violence in The Iliad") +
  theme(plot.title = element_text(size = rel(3)))

… with labels

label_colors <- c(prismatic::clr_lighten("blue", 0.7),
                  prismatic::clr_lighten("red", 0.7))
out <- il_tidy |>
  activate(nodes) |>
  mutate(centrality = centrality_degree(mode = "out")) |>
  ggraph(layout = "graphopt") +
  geom_edge_link(aes(start_cap = label_rect(node1.name),
                     end_cap = label_rect(node2.name)),
                 arrow = arrow(length = unit(1.5, 'mm'))) +
  geom_node_point(aes(color = affil)) +
  scale_color_manual(values = c("blue", "red"),
                     labels = c("Athenian", "Trojan")) +
  guides(color = "none", fill = "none") +
  geom_node_label(aes(filter = centrality > 0,
                      label = name, fill = affil),
                      size = rel(2.5)) +
  scale_fill_manual(values = label_colors) +
  labs(title = "Violence in The Iliad") +
  theme(plot.title = element_text(size = rel(3)))

Betweenness centrality

out <- il_tidy |>
  activate(nodes) |>
  mutate(centrality = centrality_degree(),
         betweenness = centrality_betweenness()) |>
  as_tibble() |>
  arrange(desc(betweenness)) |>
  top_n(10, wt = betweenness) |>
  ggplot(mapping = aes(x = betweenness,
                       y = reorder(name,
                       betweenness), color = affil)) +
  geom_point(size = 3) +
  labs(x = "Betweenness", y = NULL, color = "Side") +
  theme_minimal() +
  theme(legend.position = "top")

Sarcophagus

]

Alpha centrality

out <- il_tidy |>
  activate(edges) |>
  filter(act == "kills") |>
  reroute(from = to, to = from) |>
  activate(nodes) |>
  mutate(alpha = centrality_alpha()) |>
  as_tibble() |>
  arrange(desc(alpha)) |>
    top_n(10, wt = alpha) |>
  ggplot(mapping = aes(x = alpha,
                       y = reorder(name, alpha),
                       color = affil)) +
  geom_point(size = 3) +
  labs(x = "Alpha Centrality", y = NULL, color = "Side") +
  theme_minimal() +
  theme(legend.position = "top")