Recap affiliation and one-mode network
Let’s organize the data one more time. I’m gonna work again with the one-matrix (actorxactor). As you might remember, this one-mode matrix is a projection of the affiliation network (actorxcase), which means that the actors (the nodes) are tied by virtue of their participation in the same cases.
#Affiliation network data
library(igraph)
library(tidyr)
data <- read.csv("Cleaned_Data.csv")
##New column count
data$count <- 1
##Gather the data at case level
lev_data <- pivot_wider(data,id_cols = CaseID, names_from = `Name`,
values_from = count, values_fn = list(count = length),
values_fill = list(count = 0))
##transpose lev_data to have amici grouped by case
library(data.table)
T_lev_data <- transpose(lev_data,)
rownames(T_lev_data) <- colnames(lev_data)
colnames(T_lev_data) <- lev_data$CaseID
T_lev_data <- T_lev_data[-c(1),]
##create affiliation network graph using 'igraph'
Aff_network <- graph.incidence(T_lev_data)
############
#One-Mode matrix (actor x actor)
##extracting the one-mode projection
Aff_network.pr <- bipartite.projection(Aff_network)
##Actor x actor adjacency matrix
amici_net <- Aff_network.pr$proj1
amici_ad <- graph.adjacency(get.adjacency(amici_net, sparse = FALSE,attr = "weight"))
Centrality measures by node (amici)
Let’s obtain the centrality measures by node in order to compare them with the betweenness scores:
library(dplyr)
#dataframe for the nodes + degree
amici.nodes<-data.frame(name=V(amici_ad)$name, degree=igraph::degree(amici_ad))
amici.nodes <- subset(amici.nodes, select = -name)
#eigenvector centrality
temp<-centr_eigen(amici_ad,directed=F)
amici.nodes$eigen<-temp$vector
#bonacich power centrality
amici.nodes$bonpow <- power_centrality(amici_ad, exponent = 0.9)
#top 5 eigenvector centrality
amici.nodes%>%
arrange(desc(eigen))%>%
slice(1:5)
degree eigen bonpow
Yale University 192 1.0000000 -0.6392321
DEJUSTICIA 218 0.9886959 -0.6535497
Center for Reproductive Rights 116 0.9051396 -0.5626440
UNAM 134 0.8920983 -0.5961262
Loyola Law School 114 0.8841434 -0.4763785First, the eigenvector centrality is showing what actors are linked to other well connected actors. In terms of this network, the eigenvector centrality allow us to see what amici actors focus their participation on ‘popular’ cases, cases that atract interventions from well connected amici. We cannot say if their ‘strategic’ behavior is driven by the other participants (du to their popularity) or the impact of the substantive matter discussed in these cases.
On the other hand, the bonacich power centrality shows the actors that participated on the cases were no other people participated (therefore the actors with greater power of influence). All of these actrs has the same bonachich power score probably because they all filed a brief only once, for a case which wasn’t of interest for other actors:
degree eigen
International Legal Advisors Esq. 2 0
Foundation for the Development of International Law 2 0
The International Commission of Jurists 2 0
Catalina Martinez Coral 2 0
Fundacion Vida Solidaria 2 0
bonpow
International Legal Advisors Esq. 3.927038
Foundation for the Development of International Law 3.927038
The International Commission of Jurists 3.927038
Catalina Martinez Coral 3.927038
Fundacion Vida Solidaria 3.927038Betwenness centrality and network constraint
In order to find the most influential actors in the amici network, it is is necessary to calculate both de closeness and betweenness centrality measures. The closeness centrality calculates the shortest paths between all nodes, then assigns each node a score based on its sum of shortest paths, this can help find good ‘broadcasters’. Meanwhile, betweenness centrality measures the number of times a node lies on the shortest path between other nodes, which can help us to find the actors who influence the flow around a system.
We might expect that international organizations and well-funded actors have a greater participation in the Inter-American system, with an influential role among local and less endowed actors.
#Closeness centrality
amici.nodes$close <- igraph::closeness(amici_ad)
amici.nodes%>%
arrange(desc(close))%>%
slice(1:5)
degree eigen bonpow
Women's Link Worldwide 66 0.0933683 -0.6017687
Yale University 192 1.0000000 -0.6392321
UNAM 134 0.8920983 -0.5961262
Center for Reproductive Rights 116 0.9051396 -0.5626440
Interights 110 0.8835159 -1.4061725
close
Women's Link Worldwide 2.049516e-05
Yale University 2.049138e-05
UNAM 2.048509e-05
Center for Reproductive Rights 2.047251e-05
Interights 2.047167e-05#Betweenness centrality
amici.nodes$between<-igraph::betweenness(amici_ad, directed=FALSE)
amici.nodes%>%
arrange(desc(between))%>%
slice(1:5)
degree eigen bonpow close
Women's Link Worldwide 66 0.093368302 -0.6017687 2.049516e-05
CEJIL 138 0.003024349 -0.6255743 2.045617e-05
Yale University 192 1.000000000 -0.6392321 2.049138e-05
Amnesty International 96 0.002862279 -0.7003592 2.044739e-05
UNAM 134 0.892098273 -0.5961262 2.048509e-05
between
Women's Link Worldwide 14257.860
CEJIL 9557.596
Yale University 8762.995
Amnesty International 8186.167
UNAM 7470.614As expected, international actors such as Amnesty International, Women’s Link Worldwide, and Interights are among the most influential actors. Likewise, although local, Yale University and the National Autonomous University of Mexico (UNAM) are a good example of well-funded organization with enough capacity to influence the Inter-American system. Furthermore, CEJIL (Center for Justice and International Law) is precisely an organization aimed to contribute to the “full enjoyment of human rights in the Americas through the effective use of Inter-American System tools and other international human rights law protection mechanisms”.
As we can see, these centrality measures provide a better understanding of the most influential actors in the IAcHR network. Because this is a ‘undirected’ network, we cannot provide any measures of brockerage.
