Introduction

Representing the geopolitical context of the cold war period and after it ended through a network is an riveting way of approaching this historical interval in a mathematical way, therefore, if we understand the actors of international relations (States) as nodes of a network

Loading libraries

library("network")
library("ggnetwork")
library("sna")
library("dplyr")
library("knitr")
library("tibble")
library("ggrepel")



setwd("C:/Users/jebet/OneDrive/Escritorio/UEXT/ULB/Social network analysis/Directory")
all_data <- read.table("alliance_v4.1_by_dyad.csv", sep=",", header=TRUE, na.strings="", stringsAsFactors = FALSE)
View(all_data)

Functions

We made many functions in order to create easier subsets an to be able to use the measures.

subseting <- function(start_d, end_d){

  sub <- subset(all_data,
                     asymmetric == 0 & defense == 1 &
                       (dyad_st_year <= end_d | (is.na(dyad_st_year) & left_censor == 1)) & 
                       (dyad_end_year >= start_d | (is.na(dyad_end_year) & right_censor == 1)))

  country_codes <- sort(unique(c(sub$ccode1, sub$ccode2)))
  N <- length(country_codes)
  
  sub$snd <- match(sub$ccode1, country_codes)
  sub$rec <- match(sub$ccode2, country_codes)
  sub$val <- 1
  sub_edges <- sub[, c("snd", "rec", "val")]
  
  country_names_all <- data.frame(ccode = c(sub$ccode1, sub$ccode2),
                                  state = c(as.character(sub$state_name1),
                                            as.character(sub$state_name2)),
                                  stringsAsFactors = FALSE)
  
  country_names_table <- sort(unique(country_names_all))
  country_names <- country_names_table$state[match(country_codes, country_names_table$ccode)]
  
  sub_edges_b <- unique(sub_edges)
  sub_edgelist <- as.matrix(sub_edges_b) 

  attr(sub_edgelist, "n") <- N
  attr(sub_edgelist, "vnames") <- country_names
  
  sub_mat <- as.sociomatrix.sna(sub_edgelist)
  sub_net <- as.network(sub_edgelist, matrix.type = "edgelist", directed = FALSE, multiple = FALSE, edge.check = TRUE) 
}
  
plot_that <- function(sub,sub_title=""){
  
  ggplot(sub, aes(x = x, y = y, xend = xend, yend = yend)) +
    ggtitle(sub_title)+
    geom_edges(alpha = 0.5, colour = "lightgray", size = 1) +
    geom_nodetext_repel(mapping = aes(label = vertex.names),force = 5) + 
    geom_nodes() +
    theme_blank() 

  
}

central_mat <- function(sub_mat){
  
  n_sub_mat <- nrow(sub_mat)
  base_sub_df <- data.frame(Country = rownames(sub_mat), 
                            Degree = degree(sub_mat, gmode = "graph"),
                            StdDegree = degree(sub_mat, gmode = "graph")/(n_sub_mat-1),  
                            Betweenness = betweenness(sub_mat, gmode = "graph"),
                            StdBetweenness = betweenness(sub_mat, gmode = "graph")/((n_sub_mat-1)*(n_sub_mat-2)/2), stringsAsFactors = FALSE) 

}

Subsets creation

We make the following to test some subsets.

cw_net <- subseting(1946,1989)
now_net <- subseting(1991,2012)

cw_mat <- as.sociomatrix.sna(cw_net)
now_mat <- as.sociomatrix.sna(now_net)

cw_ego <- ego.extract(cw_net)
now_ego <- ego.extract(now_net)

Adding plots

set.seed(4)
cw_coord <- fortify(cw_net, layout = "kamadakawai")
now_coord <- fortify(now_net)

plot_that(cw_coord, "Network Showing Aliances during Cold War (1947-1991)")

plot_that(now_coord, "Network Showing Aliances Between 1990 and 2012")

Centrality measures

Following the network that we plotted, it is imperative to understand the measures that come within this data set, therefore, understanding the 10 countries with elevated quantities of Degree, Betweenness and Closeness.

base_cw_df <- central_mat(cw_mat)
base_now_df <- central_mat(now_mat)

sort_cw_df <- base_cw_df[order(base_cw_df$StdBetweenness ,decreasing = TRUE),]
sort_now_df <- base_now_df[order(base_now_df$StdBetweenness ,decreasing = TRUE),]
sort_cw_df1 <- base_cw_df[order(base_cw_df$StdBetweenness ,decreasing = TRUE),]
sort_now_df1 <- base_now_df[order(base_now_df$StdBetweenness ,decreasing = TRUE),]
sort_cw_df2 <- base_cw_df[order(base_cw_df$StdDegree ,decreasing = TRUE),]
sort_now_df2 <- base_now_df[order(base_now_df$StdDegree ,decreasing = TRUE),]
 

kable(sort_cw_df1[1:10,], digits = 2, caption = "Betweenness cw")
Betweenness cw
Country Degree StdDegree Betweenness StdBetweenness
38 France 19 0.17 1842.17 0.31
1 United States of America 48 0.44 1802.67 0.30
34 United Kingdom 17 0.15 1646.62 0.27
93 Iraq 18 0.16 1298.36 0.22
52 Russia 15 0.14 1061.99 0.18
2 Canada 39 0.35 925.00 0.15
63 Mauritania 26 0.24 480.63 0.08
74 Gabon 14 0.13 341.66 0.06
75 Central African Republic 14 0.13 341.66 0.06
76 Chad 14 0.13 341.66 0.06 
kable(sort_now_df1[1:10,], digits = 2, caption = "Betweenness now")
Betweenness now
Country Degree StdDegree Betweenness StdBetweenness
39 France 19 0.15 2500.33 0.33
82 Gabon 11 0.09 2499.00 0.33
102 Sudan 26 0.21 2211.00 0.29
71 Mauritania 19 0.15 1275.00 0.17
1 United States of America 46 0.37 1142.00 0.15
2 Canada 44 0.35 945.00 0.12
85 Congo 17 0.14 448.00 0.06
94 Angola 17 0.14 448.00 0.06
83 Central African Republic 15 0.12 351.00 0.05
86 Democratic Republic of the Congo 15 0.12 351.00 0.05 
kable(sort_cw_df2[1:10,], digits = 2, caption = "StdDegree cw")
StdDegree cw
Country Degree StdDegree Betweenness StdBetweenness
1 United States of America 48 0.44 1802.67 0.30
2 Canada 39 0.35 925.00 0.15
5 Haiti 31 0.28 4.67 0.00
6 Dominican Republic 31 0.28 4.67 0.00
16 Mexico 31 0.28 4.67 0.00
17 Guatemala 31 0.28 4.67 0.00
18 Honduras 31 0.28 4.67 0.00
20 Nicaragua 31 0.28 4.67 0.00
21 Costa Rica 31 0.28 4.67 0.00
22 Panama 31 0.28 4.67 0.00 
kable(sort_now_df2[1:10,], digits = 2, caption  = "StdDegree now")
StdDegree now
Country Degree StdDegree Betweenness StdBetweenness
1 United States of America 46 0.37 1142 0.15
2 Canada 44 0.35 945 0.12
3 Bahamas 28 0.23 0 0.00
4 Haiti 28 0.23 0 0.00
5 Dominican Republic 28 0.23 0 0.00
6 Jamaica 28 0.23 0 0.00
8 Barbados 28 0.23 0 0.00
9 Dominica 28 0.23 0 0.00
10 Grenada 28 0.23 0 0.00
11 St. Lucia 28 0.23 0 0.00 
ten_cw_df <- sort_cw_df[1:10,]
ten_now_df <- sort_now_df[1:10,]

Centrality graphs

It is highly pertinent to perceive the formal and informal power that certain countries can generate in the network, the graph shows in a mathematical order how particular countries can influence their corresponding alliances, for example, countries such as United States of America showcase great influence during and after the cold war period, meanwhile, Russia, United Kingdom and Iraq lose exposure and negotiation capacity after the conflict.

ggplot(data = ten_cw_df, aes(x =  StdBetweenness, y =StdDegree , label = Country)) +
  geom_point()+
  geom_label_repel(size = 5)

ggplot(data = ten_now_df, aes(x =  StdBetweenness, y =StdDegree , label = Country)) +
  geom_point()+
  geom_label_repel(size = 5)

StdBetweenes Network

Betweennes measure showcases how countries influence a group of other countries through their alliances or agreements. In general, the following graphs prove that after the cold war period, countries’ nodes lie shorter from each other which means a higher control of diplomatic information between countries and the materialization of informal power as it is.

ten_cw_country <- ten_cw_df$Country
ten_now_country <- ten_now_df$Country

ten_cw_mat <- cw_mat[ten_cw_country,ten_cw_country]
ten_cw_net <- as.network(ten_cw_mat,  directed = FALSE, multiple = FALSE, edge.check = TRUE)

ten_now_mat <- now_mat[ten_now_country,ten_now_country]
ten_now_net <- as.network(ten_now_mat,  directed = FALSE, multiple = FALSE, edge.check = TRUE) 


plot_that(ten_cw_net, "Most StdBetweeness during the Cold War")

plot_that(ten_now_net,"Most StdBetweeness 1990 - 2012")

#We have here graphical representation of the countries with considerable betweenness during the cold war and afterwards its culmination. The graphs indicating the conflict period are labeled as "cw". 

plot_that(ggnetwork(cw_ego$France),"France cw") 

plot_that(ggnetwork(now_ego$France),"France")

plot_that(ggnetwork(cw_ego$`United States of America`),"United States of America cw")

plot_that(ggnetwork(now_ego$`United States of America`),"United States of America")

plot_that(ggnetwork(cw_ego$`United Kingdom`),"United Kingdom cw")

plot_that(ggnetwork(now_ego$`United Kingdom`),"United Kingdom")

plot_that(ggnetwork(cw_ego$Russia),"Russia cw")

plot_that(ggnetwork(now_ego$Russia),"Russia")

Conclusion

#library("igraph")
#library("remotes")
#library("RBioFabric")


#cw_graph <- intergraph::asIgraph(cw_net)

#class(cw_graph)

#bioFabric(cw_graph)



#for (variable in ten_cw_country) {
  
#}





#test <- cliques(cw_graph,max=25)

#plot_that(test)