Practice Exercise: Computing Centrality Measures

Week 2 - Network Analytics

Exercise Overview

Task: Calculate centrality measures for a collaboration network and interpret the results.

Network Description:

• 15-node collaboration network
• Undirected edges (mutual relationships)
• Nodes represent team members
• Edges represent working relationships

Questions

1. Which node has the highest degree centrality?
2. Which node has the highest betweenness centrality?
3. Which node has the highest closeness centrality?
4. Which nodes have the highest clustering coefficient?
5. How do these metrics correlate with each other?

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Network Initialization and Visualization

library(igraph)
library(ggraph)

# Create a larger exercise network (15 nodes)
set.seed(999)
edges_exercise <- data.frame(
  from = c(1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 13, 13, 14),
  to = c(2, 3, 4, 3, 5, 4, 5, 5, 6, 6, 7, 8, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15)
)

g_exercise <- graph_from_data_frame(edges_exercise, directed = FALSE)

# Plot the network
ggraph(g_exercise, layout = 'fr') +
  geom_edge_link(color = "#D3D3D3", width = 1.5, alpha = 0.6) +
  geom_node_point(color = "#c41c85", size = 12) +
  geom_node_text(aes(label = name), color = "white", size = 4) +
  scale_x_continuous(expand = expansion(mult = 0.2)) +
  scale_y_continuous(expand = expansion(mult = 0.2)) +
  theme_void() +
  theme(
    plot.background = element_rect(fill = "white", color = NA)
  )