Exercise 2 - Fakebook Bus

# Create edge list representing seat adjacency
edge_list <- data.frame(
  from = c("A", "A","A", "B", "B", "B", "B", "C", "C", "C", "C", "C", "D", "D", "D", "D", "D"),
  to = c("2", "B","C", "A", "D", "C", "6", "B", "A", "D", "3", "4", "5", "6", "3", "B", "C")
)

print(edge_list)

##    from to
## 1     A  2
## 2     A  B
## 3     A  C
## 4     B  A
## 5     B  D
## 6     B  C
## 7     B  6
## 8     C  B
## 9     C  A
## 10    C  D
## 11    C  3
## 12    C  4
## 13    D  5
## 14    D  6
## 15    D  3
## 16    D  B
## 17    D  C

# Load network analysis library
library(igraph)

## Warning: 程辑包'igraph'是用R版本4.3.3 来建造的

## 
## 载入程辑包：'igraph'

## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum

## The following object is masked from 'package:base':
## 
##     union

# Create graph object
bus_graph <- graph_from_data_frame(edge_list, directed = FALSE) 

# Function to calculate centrality for a given vertex
calculate_centrality <- function(graph, vertex) {
  data.frame(
    degree = degree(graph, vertex),
    closeness = closeness(graph, vertex),
    betweenness = betweenness(graph, vertex)
  )
}

# Calculate centrality for each open seat
centrality_A <- calculate_centrality(bus_graph, "A")
centrality_B <- calculate_centrality(bus_graph, "B")
centrality_C <- calculate_centrality(bus_graph, "C")
centrality_D <- calculate_centrality(bus_graph, "D")

# Display the results
print(centrality_A); 

##   degree  closeness betweenness
## A      5 0.07142857           7

print(centrality_B); 

##   degree  closeness betweenness
## B      7 0.08333333           5

print(centrality_C); 

##   degree  closeness betweenness
## C      8 0.09090909        11.5

print(centrality_D)

##   degree  closeness betweenness
## D      7 0.08333333         9.5

# Put results in dataframe
centrality <- data.frame(rbind(centrality_A,centrality_B,centrality_C, centrality_D))
print(centrality)

##   degree  closeness betweenness
## A      5 0.07142857         7.0
## B      7 0.08333333         5.0
## C      8 0.09090909        11.5
## D      7 0.08333333         9.5

Considering all three measures of centrality, C is the seat that has the maximum reach in the network. Therefore I would pick seat C. Below is a graph of the network with each vertex representing a seat.

# Set vertex labels according to seats
V(bus_graph)$label <- V(bus_graph)$name

# Plot the graph with centrality size and labels
plot(bus_graph, vertex.size = degree(bus_graph) * 5, vertex.label = V(bus_graph)$label)