Challenge 2 Mekhala

challenge_2

Mekhala Kumar

got like_dislike

Describing the Basic Structure of a Network

Author

Mekhala Kumar

Published

March 24, 2023

Reading in the data

Code

like_dislike<-read_csv("_data/got/got_like_dislike.csv")

Rows: 46 Columns: 49
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr  (3): Current house, Former house, Name
dbl (46): Lysa Arryn, Petyr Baelish, Joffrey Baratheon, Margaery Tyrell, Ren...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Code

head(like_dislike)

# A tibble: 6 × 49
  Curren…¹ Forme…² Name  Lysa …³ Petyr…⁴ Joffr…⁵ Marga…⁶ Renly…⁷ Rober…⁸ Stann…⁹
  <chr>    <chr>   <chr>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
1 Arryn    Tully   Lysa…      NA       3       0       0       0       1       0
2 Baelish  <NA>    Pety…       3      NA      -1       1      -2       1      -1
3 Lannist… Barath… Joff…       0      -1      NA       4      -3       2      -5
4 Tyrell   Barath… Marg…       0       1       3      NA       5       0      -5
5 Barathe… <NA>    Renl…       0      -2      -5       5      NA       3      -5
6 Barathe… <NA>    Robe…       2       1       4       0       3      NA       2
# … with 39 more variables: `Brienne of Tarth` <dbl>, Bronn <dbl>,
#   `Gregor Clegane` <dbl>, `Sandor Clegane` <dbl>, `Xaro Xhoan Daxos` <dbl>,
#   Gendry <dbl>, `Balon Greyjoy` <dbl>, `Theon Greyjoy` <dbl>,
#   `Jaqen H'ghar` <dbl>, Hodor <dbl>, `Khal Drogo` <dbl>,
#   `Cersei Lannister` <dbl>, `Jaime Lannister` <dbl>,
#   `Lancel Lannister` <dbl>, `Tyrion Lannister` <dbl>,
#   `Tywin Lannister` <dbl>, `Maester Luwin` <dbl>, Melisandre <dbl>, …

Converting into Network data format

In the adjacency matrix I looked for which values had an edge to compare the number of edges reported once the network is created.

Code

adj<-subset(like_dislike[4:49])
vertex_names<-colnames(adj)
row.names(adj) <- vertex_names

Warning: Setting row names on a tibble is deprecated.

Code

adj_mat <- data.matrix(adj)
#diag(adj_mat) <- 0
table(adj_mat != 0)


FALSE  TRUE 
  927  1143

Code

#igraph
like_dislike.net <- graph_from_adjacency_matrix(adj_mat, mode = "directed", weighted = TRUE, diag = FALSE)
V(like_dislike.net)$name

 [1] "Lysa Arryn"            "Petyr Baelish"         "Joffrey Baratheon"    
 [4] "Margaery Tyrell"       "Renly Baratheon"       "Robert Baratheon"     
 [7] "Stannis Baratheon"     "Brienne of Tarth"      "Bronn"                
[10] "Gregor Clegane"        "Sandor Clegane"        "Xaro Xhoan Daxos"     
[13] "Gendry"                "Balon Greyjoy"         "Theon Greyjoy"        
[16] "Jaqen H'ghar"          "Hodor"                 "Khal Drogo"           
[19] "Cersei Lannister"      "Jaime Lannister"       "Lancel Lannister"     
[22] "Tyrion Lannister"      "Tywin Lannister"       "Maester Luwin"        
[25] "Melisandre"            "Jeor Mormont"          "Jorah Mormont"        
[28] "Osha"                  "Podrick Payne"         "Pyat Pree"            
[31] "Grand Maester Pycelle" "Ros"                   "Davos Seaworth"       
[34] "Shae"                  "Jon Snow"              "Arya Stark"           
[37] "Bran Stark"            "Catelyn Stark"         "Robb Stark"           
[40] "Sansa Stark"           "Daenerys Targaryen"    "Viserys Targaryen"    
[43] "Samwell Tarly"         "Loras Tyrell"          "Varys"                
[46] "Eddard Stark"

Code

#statnet
like_dislike_statnet <- network(adj_mat,matrix.type="adjacency", directed=TRUE, loops = FALSE)

Describe the Network Data

The network has 46 vertices and 1143 edges. It is unimodal, directed and weighted. I tried the commands both in igraph and statnet because initially I was getting different number of edges for the two so I wanted to check if there were any inconsistencies remaining.

Code

#igraph
vcount(like_dislike.net)

[1] 46

Code

ecount(like_dislike.net)

[1] 1143

Code

is_bipartite(like_dislike.net)

[1] FALSE

Code

is_directed(like_dislike.net)

[1] TRUE

Code

is_weighted(like_dislike.net)

[1] TRUE

Code

vertex_attr_names(like_dislike.net)

[1] "name"

Code

edge_attr_names(like_dislike.net)

[1] "weight"

Code

V(like_dislike.net)$name

 [1] "Lysa Arryn"            "Petyr Baelish"         "Joffrey Baratheon"    
 [4] "Margaery Tyrell"       "Renly Baratheon"       "Robert Baratheon"     
 [7] "Stannis Baratheon"     "Brienne of Tarth"      "Bronn"                
[10] "Gregor Clegane"        "Sandor Clegane"        "Xaro Xhoan Daxos"     
[13] "Gendry"                "Balon Greyjoy"         "Theon Greyjoy"        
[16] "Jaqen H'ghar"          "Hodor"                 "Khal Drogo"           
[19] "Cersei Lannister"      "Jaime Lannister"       "Lancel Lannister"     
[22] "Tyrion Lannister"      "Tywin Lannister"       "Maester Luwin"        
[25] "Melisandre"            "Jeor Mormont"          "Jorah Mormont"        
[28] "Osha"                  "Podrick Payne"         "Pyat Pree"            
[31] "Grand Maester Pycelle" "Ros"                   "Davos Seaworth"       
[34] "Shae"                  "Jon Snow"              "Arya Stark"           
[37] "Bran Stark"            "Catelyn Stark"         "Robb Stark"           
[40] "Sansa Stark"           "Daenerys Targaryen"    "Viserys Targaryen"    
[43] "Samwell Tarly"         "Loras Tyrell"          "Varys"                
[46] "Eddard Stark"

Code

#statnet
print(like_dislike_statnet)

 Network attributes:
  vertices = 46 
  directed = TRUE 
  hyper = FALSE 
  loops = FALSE 
  multiple = FALSE 
  bipartite = FALSE 
  total edges= 1143 
    missing edges= 0 
    non-missing edges= 1143 

 Vertex attribute names: 
    vertex.names 

 Edge attribute names not shown

Dyad and Triad Census

There are 554 mutual connections, 35 non-mutual connections and 446 nodes which are not connected.

Code

igraph::dyad.census(like_dislike.net)

$mut
[1] 554

$asym
[1] 35

$null
[1] 446

Code

sna::dyad.census(like_dislike_statnet)

     Mut Asym Null
[1,] 554   35  446

Triad Census

Code

igraph::triad_census(like_dislike.net)

 [1] 1780  308 4637    5   11   22  222  285    1    1 3849    8   19   26  537
[16] 3469

Code

sna::triad.census(like_dislike_statnet, mode="graph")

        0    1    2    3
[1,] 1975 5109 4405 3691

Global and Local Transitivity or Clustering

The global transitivity is slightly smaller than the average local clustering coefficient. This shows on average, the density globally is comparable to the density for the local ego networks.

Code

#Global
transitivity(like_dislike.net, type="global")

[1] 0.7349339

Code

##Average local clustering coefficient
transitivity(like_dislike.net, type="average")

[1] 0.754549

Code

gtrans(like_dislike_statnet)

[1] 0.7184677

It can be seen that the density for Ros’ network higher in comparison to the density across the network whereas the density for Arya Stark’s and Bronn’s networks are comparable to the global and average clustering coefficients.

Code

#Local
V(like_dislike.net)[c("Arya Stark","Ros", "Bronn")]

+ 3/46 vertices, named, from c2734b5:
[1] Arya Stark Ros        Bronn

Code

transitivity(like_dislike.net,type="local",vids=V(like_dislike.net)[c("Arya Stark","Ros", "Bronn")])

[1] 0.7045455 0.8888889 0.7632184

Path Length, Geodesic and Component Structure

I looked into the shortest paths and distances between a few of the people.

Code

all_shortest_paths(like_dislike.net,from="Ros",to="Jon Snow", mode="out",weights=NA)$res

[[1]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros              Cersei Lannister Jon Snow        

[[2]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros           Theon Greyjoy Jon Snow     

[[3]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros              Robert Baratheon Jon Snow        

[[4]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros               Joffrey Baratheon Jon Snow

Code

all_shortest_paths(like_dislike.net,from="Ros",to="Jon Snow", mode="in",weights=NA)$res

[[1]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros              Cersei Lannister Jon Snow        

[[2]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros           Theon Greyjoy Jon Snow     

[[3]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros              Robert Baratheon Jon Snow        

[[4]]
+ 3/46 vertices, named, from c2734b5:
[1] Ros               Joffrey Baratheon Jon Snow

Code

all_shortest_paths(like_dislike.net,from="Bronn",to="Arya Stark", mode="in",weights=NA)$res

[[1]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn        Eddard Stark Arya Stark  

[[2]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn      Varys      Arya Stark

[[3]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn        Loras Tyrell Arya Stark  

[[4]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn             Viserys Targaryen Arya Stark       

[[5]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn              Daenerys Targaryen Arya Stark        

[[6]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn       Sansa Stark Arya Stark 

[[7]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn      Robb Stark Arya Stark

[[8]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn         Catelyn Stark Arya Stark   

[[9]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn          Davos Seaworth Arya Stark    

[[10]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn         Jorah Mormont Arya Stark   

[[11]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn      Melisandre Arya Stark

[[12]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn           Tywin Lannister Arya Stark     

[[13]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn           Jaime Lannister Arya Stark     

[[14]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn            Cersei Lannister Arya Stark      

[[15]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn         Theon Greyjoy Arya Stark   

[[16]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn      Gendry     Arya Stark

[[17]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn          Gregor Clegane Arya Stark    

[[18]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn            Brienne of Tarth Arya Stark      

[[19]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn             Stannis Baratheon Arya Stark       

[[20]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn             Joffrey Baratheon Arya Stark       

[[21]]
+ 3/46 vertices, named, from c2734b5:
[1] Bronn         Petyr Baelish Arya Stark

Code

distances(like_dislike.net,v="Bronn",to="Ros",weights=NA,algorithm="johnson")

      Ros
Bronn   2

Code

distances(like_dislike.net,v="Bronn",to="Arya Stark",weights=NA,algorithm="johnson")

      Arya Stark
Bronn          2

Code

distances(like_dislike.net,v="Arya Stark",to="Jon Snow",weights=NA,algorithm="johnson")

           Jon Snow
Arya Stark        1

Average path length

Since this network has negative weights, I was unable to use the commands for average path length and diameter directly. Hence, I converted the values by adding 10 to each observation to make the values positive. This made the original neutral connections equal to 10 which I changed back to 0 in order to avoid confusion regarding the distances calculated.

Code

new_adj<-adj_mat+10
new_adj[new_adj == 10] <- 0
like_dislike2 <- graph_from_adjacency_matrix(new_adj, mode = "directed", weighted = TRUE, diag = FALSE)

average.path.length(like_dislike2,directed=T)

[1] 11.24589

Code

diameter(like_dislike2)

[1] 24

Component Structure

This network consists of a single component with 46 members.

Code

names(igraph::components(like_dislike.net))

[1] "membership" "csize"      "no"

Code

#igraph::components(like_dislike.net)$membership #very long list
igraph::components(like_dislike.net)$no

[1] 1

Code

igraph::components(like_dislike.net)$csize

[1] 46

There are no isolates in this network.

Code

isolates(like_dislike_statnet)

integer(0)

Plot

Code

plot(like_dislike.net)

Warning in v(graph): Non-positive edge weight found, ignoring all weights
during graph layout.