Game of Thrones Marriages
plot.igraph(gotmarr.ig,
vertex.label.cex=1)
Network Size
Attributes
is_bipartite(gotmarr.ig)
[1] FALSEis_directed(gotmarr.ig)
[1] FALSEis_weighted(gotmarr.ig)
[1] TRUEvertex_attr_names(gotmarr.ig)
[1] "color" "na" "region" "vertex.names"
[5] "name" edge_attr_names(gotmarr.ig)
[1] "na" "weight"Community Detection
Fast and greedy
#Run clustering algorithm: fast_greedy
got.fg<-cluster_fast_greedy(gotmarr.ig)
#Retrieve list of nodes in communities
igraph::groups(got.fg)
$`1`
[1] "Arryn" "Tully" "Vale"
$`2`
[1] "Martell" "Crownlands" "Essos" "Targaryen" "Dorne"
$`3`
[1] "Baratheon" "Reach" "Tyrell"
$`4`
[1] "Stormlands" "Riverlands" "Frey"
$`5`
[1] "Lannister" "Westerlands"
$`6`
[1] "Stark" "North"plot(got.fg,gotmarr.ig)
Walktrap
nodes.by.gp<-function(network.nodes, groupvar){
network.nodes%>%
select(-name)%>%
group_by_(groupvar) %>%
mutate(n=n())%>%
summarise_all(mean, na.rm=TRUE)%>%
as.matrix()%>%
print(digits=2)
}
got.wt<-walktrap.community(gotmarr.ig)
igraph::groups(got.wt)
$`1`
[1] "Arryn" "Tully" "Vale" "Stormlands" "Riverlands"
[6] "Frey"
$`2`
[1] "Martell" "Crownlands" "Essos" "Targaryen" "Dorne"
$`3`
[1] "Baratheon" "Reach" "Tyrell"
$`4`
[1] "Stark" "North"
$`5`
[1] "Lannister" "Westerlands"gotmarr.nodes$comm.wt<-got.wt$membership
nodes.by.gp(gotmarr.nodes,"comm.wt")
comm.wt degree degree.wt bonpow betweenness close constraint n
[1,] 1 5.5 23 -1.31 4.5 0.58 0.41 6
[2,] 2 5.2 22 -0.79 9.3 0.57 0.62 5
[3,] 3 6.0 22 -0.96 8.9 0.59 0.45 3
[4,] 4 6.0 36 -0.29 6.9 0.59 0.53 2
[5,] 5 5.5 25 -0.15 1.4 0.58 0.57 2plot(got.wt,gotmarr.ig)
Label Propagation
got.lab<-walktrap.community(gotmarr.ig)
igraph::groups(got.lab)
$`1`
[1] "Arryn" "Tully" "Vale" "Stormlands" "Riverlands"
[6] "Frey"
$`2`
[1] "Martell" "Crownlands" "Essos" "Targaryen" "Dorne"
$`3`
[1] "Baratheon" "Reach" "Tyrell"
$`4`
[1] "Stark" "North"
$`5`
[1] "Lannister" "Westerlands"gotmarr.nodes$comm.lab<-got.lab$membership
nodes.by.gp(gotmarr.nodes,"comm.lab")
comm.lab degree degree.wt bonpow betweenness close constraint
[1,] 1 5.5 23 -1.31 4.5 0.58 0.41
[2,] 2 5.2 22 -0.79 9.3 0.57 0.62
[3,] 3 6.0 22 -0.96 8.9 0.59 0.45
[4,] 4 6.0 36 -0.29 6.9 0.59 0.53
[5,] 5 5.5 25 -0.15 1.4 0.58 0.57
comm.wt n
[1,] 1 6
[2,] 2 5
[3,] 3 3
[4,] 4 2
[5,] 5 2plot(got.lab,gotmarr.ig)
Edge betweeness
got.edge<-edge.betweenness.community(gotmarr.ig)
igraph::groups(got.edge)
$`1`
[1] "Arryn"
$`2`
[1] "Tully"
$`3`
[1] "Vale"
$`4`
[1] "Baratheon"
$`5`
[1] "Lannister"
$`6`
[1] "Martell"
$`7`
[1] "Reach"
$`8`
[1] "Stark"
$`9`
[1] "Stormlands"
$`10`
[1] "Tyrell"
$`11`
[1] "Crownlands"
$`12`
[1] "Essos"
$`13`
[1] "Riverlands"
$`14`
[1] "Westerlands"
$`15`
[1] "Frey"
$`16`
[1] "North"
$`17`
[1] "Targaryen"
$`18`
[1] "Dorne"gotmarr.nodes$comm.edge<-got.edge$membership
nodes.by.gp(gotmarr.nodes,"comm.edge")
comm.edge degree degree.wt bonpow betweenness close constraint
[1,] 1 3 10 -1.113 0.67 0.50 0.51
[2,] 2 5 5 -1.042 2.31 0.53 0.48
[3,] 3 5 34 -1.085 2.51 0.57 0.36
[4,] 4 7 10 -0.757 10.86 0.63 0.38
[5,] 5 5 22 -0.086 0.89 0.55 0.65
[6,] 6 3 8 -0.699 0.75 0.52 0.74
[7,] 7 9 46 -1.442 15.76 0.68 0.32
[8,] 8 9 33 0.057 13.56 0.68 0.40
[9,] 9 4 10 -1.941 0.62 0.57 0.41
[10,] 10 2 11 -0.685 0.00 0.45 0.66
[11,] 11 6 17 -0.514 1.80 0.59 0.50
[12,] 12 4 10 -0.956 2.15 0.55 0.70
[13,] 13 6 32 -1.171 2.85 0.61 0.46
[14,] 14 6 28 -0.214 1.97 0.61 0.49
[15,] 15 10 48 -1.513 17.98 0.68 0.24
[16,] 16 3 39 -0.628 0.31 0.50 0.65
[17,] 17 12 73 -1.256 42.02 0.77 0.18
[18,] 18 1 2 -0.500 0.00 0.45 1.00
comm.wt comm.lab n
[1,] 1 1 1
[2,] 1 1 1
[3,] 1 1 1
[4,] 3 3 1
[5,] 5 5 1
[6,] 2 2 1
[7,] 3 3 1
[8,] 4 4 1
[9,] 1 1 1
[10,] 3 3 1
[11,] 2 2 1
[12,] 2 2 1
[13,] 1 1 1
[14,] 5 5 1
[15,] 1 1 1
[16,] 4 4 1
[17,] 2 2 1
[18,] 2 2 1plot(got.edge,gotmarr.ig)
Eigenvector
got.eigen<-leading.eigenvector.community(gotmarr.ig)
igraph::groups(got.eigen)
$`1`
[1] "Arryn" "Baratheon" "Martell" "Stormlands" "Crownlands"
[6] "Essos" "Targaryen" "Dorne"
$`2`
[1] "Tully" "Vale" "Riverlands" "Frey"
$`3`
[1] "Reach"
$`4`
[1] "Stark" "North"
$`5`
[1] "Lannister" "Westerlands"
$`6`
[1] "Tyrell"gotmarr.nodes$comm.eigen<-got.eigen$membership
nodes.by.gp(gotmarr.nodes,"comm.eigen")
comm.eigen degree degree.wt bonpow betweenness close constraint
[1,] 1 5.0 18 -0.97 7.4 0.57 0.55
[2,] 2 6.5 30 -1.20 6.4 0.60 0.38
[3,] 3 9.0 46 -1.44 15.8 0.68 0.32
[4,] 4 6.0 36 -0.29 6.9 0.59 0.53
[5,] 5 5.5 25 -0.15 1.4 0.58 0.57
[6,] 6 2.0 11 -0.69 0.0 0.45 0.66
comm.wt comm.lab comm.edge n
[1,] 1.9 1.9 9.8 8
[2,] 1.0 1.0 8.2 4
[3,] 3.0 3.0 7.0 1
[4,] 4.0 4.0 12.0 2
[5,] 5.0 5.0 9.5 2
[6,] 3.0 3.0 10.0 1plot(got.eigen,gotmarr.ig)
Modularity Scores
fastgreedy walktrap label edge eigen
0.5173683 0.3289444 0.3289444 0.2051354 0.4572361 Observations
For the GOT marriages data set, the fast/greedy, walktrap, and label propagation made the most sense in identifying communities. Fast and greedy was the most successful method due to it partitioning “Baratheon”, “Reach”, and “Tyrell” as a separate community from the northern kingdoms of “Tully” and “Arryn” where there was a weak or no relationship between the factions.
Edge betweeness failed to identify any communities within the dataset, whereas the Eigenvector failed to cluster some memberships such as the Reach being distinct from the Tyrell family (rulers of the region) and has strong marriage connections with the Baratheons.