Challenge Four

Cynthia Hester

Challenge Four

Centrality of a Network

Author

Cynthia Hester

Published

March 20, 2023

Challenge Overview

Describe the many measures of centrality of at least one network of your choice. ******************************************************************************* For Challenge Four I will use the GOT Location data.

Code

#import the data
got_locations <- "C:/Users/Bud/Desktop/DACSS_697E_Social Network Analysis_SP2023/Social_Networks_SP_2023/posts/_data/got/got_locations.csv"

# Read the CSV file into a dataframe
got_locations_data <- read.csv(got_locations)

checking out first few rows of data

Code

head(got_locations_data)

Describe the Network Data

If you have not done it before, always start by evaluating the basic structure of the network (number of edges and vertices, dyad and triad census, etc.). Create a data frame nodes with the corresponding local attributes such as degree or local transitivity.

Code

# Extracting matrix from data frame
adj_matrix <- as.matrix(got_locations_data[, -c(1:3)])

# Check if the matrix is square
if (nrow(adj_matrix) == ncol(adj_matrix)) {
  got_locations_data.ig <- graph_from_adjacency_matrix(adj_matrix, mode = 'directed', weighted = TRUE)
} else {
  print("Adjacency matrix is not square")
}

Code

if (ncol(got_locations_data) == 2) {
  # The data is an edge list
  got_locations_data.ig <- graph_from_edgelist(as.matrix(got_locations_data), directed = TRUE)
} else {
  print("The data format is not supported.")
}

Code

dim(got_locations_data)

Code

got_locations_data

                                          place          region    x    y
1                     abandoned Wilding Village beyond the wall  926  136
2                                    Acorn Hall      Riverlands  777 1227
3                                       Andalos           Essos 1517 1033
4                                       Astapor    Slaver's Bay 2670 1978
5                      West of the Iron Islands    Iron Islands  161 1050
6                                     Barrowton       the North  652  709
7                                  Bitterbridge       the Reach  770 1524
8                                Blackwater Bay      Crownlands 1021 1409
9                                       Braavos           Essos 1471  943
10                        camp around the Twins      Riverlands  775  997
11                        camp near the Trident      Riverlands  900 1158
12                                   Cape Wrath      Stormlands 1114 1704
13                                 Castle Black        the Wall  955  169
14                                 Castle Darry      Riverlands  939 1193
15                               Castle Hayford      Crownlands  955 1370
16                                 Castle Rosby      Crownlands 1017 1326
17                     Cave of Beric Dondarrion      Riverlands  987 1264
18           Cave of the Children of the Forest beyond the wall  858  128
19                     cavern in haunted forest beyond the wall  822  108
20                               Craster's Keep beyond the wall  907  131
21                               Deepwood Motte       the North  643  381
22                    deserted wildling village beyond the wall 1031  109
23                                        Dorne           Dorne  859 1876
24                                 Dothraki Sea           Essos 2774 1531
25                                  Dragonstone      Crownlands 1186 1295
26                          Dragonstone (Essos)           Essos 3021 1612
27                                    Dreadfort       the North 1024  467
28                                   Duskendale      Crownlands 1088 1284
29                                    Eastwatch        the Wall 1038  178
30          Encounter with the Brave Companions      Riverlands  904 1157
31                      field outside of Pentos           Essos 1524 1378
32            Fishing village east of God's eye      Riverlands  926 1252
33                        Fist of the First Men beyond the wall  840   92
34                            Gates of the Moon        the Vale 1022 1093
35                                 Ghoyan Drohe           Essos 1678 1401
36                                   Green Fork      Riverlands  938 1075
37                              Greywater Watch       the North  787  788
38                                Gulf of Grief    Slaver's Bay 2532 2169
39                                   Hammerhorn    Iron Islands  442 1044
40                                     Hardhome beyond the wall 1075   58
41                                    Harrenhal      Riverlands  893 1222
42                               Haunted Forest beyond the wall  916  116
43                                   High Heart      Riverlands  789 1213
44         High Road (in Mountains of the Moon)        the Vale  953 1153
45                   High Road (near the Eyrie)        the Vale 1016 1101
46          Holdfast on west shore of God's eye      Riverlands  873 1260
47                      Inn of the Kneeling Man      Riverlands  791 1141
48                   Inn south of the God's eye      Riverlands  900 1319
49                               Isle of Cedars    Slaver's Bay 2662 1883
50                           Khal Drogo's manse           Essos 1505 1385
51                               King's Landing      Crownlands 1277 1642
52  Kingsroad, a little north of King's Landing      Crownlands  984 1325
53               kingsroad, north of Winterfell       the North  938  297
54               kingsroad, south of Winterfell       the North  813  670
55                            Lhazareen village           Essos 2868 1677
56                                Little Finger        the Vale 1208  924
57                                    Lordsport    Iron Islands  484 1101
58                                          Lys           Essos 1393 1944
59                                   Maidenpool      Riverlands 1032 1251
60                                   Frostfangs beyond the wall  789  107
61                                      Meereen    Slaver's Bay 2752 1752
62                          Mill on Acorn Water       the North  793  563
63                                  Moat Cailin       the North  820  754
64                                  Mole's Town       the North  958  204
65                        Mountains of the Moon        the Vale 1021 1117
66                                Nagga's Hills    Iron Islands  423 1033
67                                     New Ghis    Slaver's Bay 2735 2350
68                                    Nightfort        the Wall 1033  171
69                           North of Harrenhal      Riverlands  893 1195
70                    North of Tumbledown tower       the North  746  352
71                                       Ny Sar           Essos 1753 1456
72                       off the coast of Dorne           Dorne 1318 1874
73                     off the coast of Valyria    Slaver's Bay 2309 2299
74                           Old Crossroads Inn      Riverlands  929 1162
75                                      Old Wyk    Iron Islands  425 1035
76                                    Oldstones      Riverlands  752 1060
77                                      Oldtown       the Reach  485 1792
78                         outside of Harrenhal      Riverlands  897 1209
79                                    Pebbleton    Iron Islands  458 1052
80                                    Pennytree      Riverlands  773 1162
81                                       Pentos           Essos 1487 1396
82                                         Pyke    Iron Islands  504 1093
83                                        Qarth           Essos 3535 2151
84                                  Queenscrown        the Wall  920  206
85                                   Quiet Isle      Riverlands  993 1207
86                               Raventree Hall      Riverlands  735 1139
87                                     Red Fork      Riverlands  793 1145
88                                    Red Waste           Essos 3004 1812
89                                     Riverrun      Riverlands  732 1177
90                                     Saltpans      Riverlands  969 1196
91                                      Seagard      Riverlands  742 1024
92                                     Selhorys           Essos 1826 1782
93                               Shield Islands       the Reach  479 1598
94                                       Skagos       the North 1183  195
95                                Skirling pass beyond the wall  801   94
96                                 Slaver's Bay    Slaver's Bay 2564 1879
97                      south of Craster's Keep beyond the wall  911  147
98                                   Stone Mill      Riverlands  770 1160
99                                  Stoney Sept      Riverlands  794 1313
100                                 Stony Shore       the North  404  593
101                                 Storm's end      Stormlands 1114 1585
102                                    Sunspear           Dorne 1208 1923
103                                  Ten Towers    Iron Islands  569 1070
104                                    The Crag     Westerlands  526 1194
105                                   the Eyrie        the Vale 1068 1062
106                              the Greenblood           Dorne 1082 1910
107                               The Peach Inn      Riverlands  790 1314
108                                 the Sorrows           Essos 1813 1642
109                                   the Twins      Riverlands  764  980
110            The Wall, spot of first invasion        the Wall  911  166
111                                the Whispers      Crownlands 1197 1214
112                 Town held by Bloody Mummers      Riverlands  936 1181
113                               Trident ferry      Riverlands  917 1174
114                            Tumbledown tower       the North  714  472
115                                Vaes Dothrak           Essos 3182 1210
116                                Vaes Tolorro           Essos 3096 1826
117                   Village between the lakes       the North  914  327
118                   Village of lord Goodbrook      Riverlands  823 1199
119             Village that rests in the trees      Riverlands  845 1210
120                                    Volantis           Essos 1909 1926
121                                Volon Therys           Essos 1874 1917
122                               Water gardens           Dorne 1199 1932
123                  Weirwood north of the Wall beyond the wall  960  156
124                             Whispering Wood      Riverlands  739 1190
125                                White Harbor       the North  913  717
126                                   Whitetree beyond the wall  930  156
127                         Wilding ambush site beyond the wall  812   92
128                                  Winterfell       the North  807  505
129                                   Wolfswood       the North  678  453
130                                      Yunkai    Slaver's Bay 2701 1812
131                              Giant's stairs beyond the wall  807   77
132                                   Milkwater beyond the wall  788   71
133                                Shadow Tower        the Wall  861  171
134                            Torrhen's Square       the North  672  583

Code

got_locations_data[1 : 4, 1 : 4]

Code

edge_list <- combn(got_locations_data$place, 2)


got_graph <- graph_from_edgelist(t(edge_list), directed = FALSE)

# Get the adjacency matrix of the graph
adj_matrix <- as_adjacency_matrix(got_graph)

# Print adjacency matrix
print(adj_matrix)

  [[ suppressing 134 column names 'abandoned Wilding Village', 'Acorn Hall', 'Andalos' ... ]]

Network Attributes

edges

Code

ecount(got_graph)

nodes

Code

#  nodes of the graph
#print(V(got_graph)$name)
vcount(got_graph)

dyad census

Code

# Calculate dyad 
dyad_census <- dyad_census(got_graph)

# Print dyad 
print(dyad_census)

triad census

Code

#  triad census
triad_census <- triad_census(got_graph)

Warning in triad_census(got_graph): At core/misc/motifs.c:1165 : Triad census
called on an undirected graph.

Code

# Print triad 
print(triad_census)

Code

print(got_graph)
summary(got_graph)

transitivity

Code

transitivity(got_graph, type = 'local')

Code

transitivity(got_graph, type = "global")

Code

transitivity(got_graph, type = "localaverage")

Code

#Directed or undirected edges verification 

is_directed(got_graph)

Code

#Bipartite or single mode network verification got locations

is_bipartite(got_graph)

Code

# Weighted or unweighted edges verification in got locations

is_weighted(got_graph)

Centrality

Code

library(igraph)

 

# betweenness centrality
V(got_graph)$betweenness <- igraph::betweenness(got_graph)

# closeness centrality
V(got_graph)$closeness <- igraph::closeness(got_graph)

# eigenvector centrality
V(got_graph)$eigen_centrality <- igraph::eigen_centrality(got_graph)$vector

# data frame for centrality measures
centrality_df <- data.frame(
  Node = V(got_graph)$name,
  Betweenness = V(got_graph)$betweenness,
  Closeness = V(got_graph)$closeness,
  Eigenvector = V(got_graph)$eigen_centrality
)

# Print the centrality table
print(centrality_df)