Week 2 Challenge - GOT Marriages - Census, Transitivity, etc

Describing the Basic Structure of a Network

Challenge Overview

Code

got_marriages = read_csv("_data/got/got_marriages.csv", show_col_types = FALSE)
got_marriages

# A tibble: 255 × 5
   From      To        Type    Notes  Generation
   <chr>     <chr>     <chr>   <chr>  <chr>     
 1 Targaryen Stark     Married R+L=J  Current   
 2 Baratheon Martell   Engaged died   Current   
 3 Baratheon Stark     Engaged broken Current   
 4 Martell   Essos     Married <NA>   Current   
 5 Martell   Reach     Affair  <NA>   Current   
 6 Martell   Essos     Affair  <NA>   Current   
 7 Martell   Essos     Affair  <NA>   Current   
 8 Martell   Septa     Affair  <NA>   Current   
 9 Martell   Dorne     Affair  <NA>   Current   
10 Martell   Targaryen Married <NA>   Current   
# … with 245 more rows

Describe the Network Data

Code

got_marriages.ig = graph_from_data_frame(got_marriages, directed = FALSE) #directed = false because with relationships, if a is married to b then b is also married to a
got_marriages.ig

IGRAPH a8a852e UN-- 20 255 -- 
+ attr: name (v/c), Type (e/c), Notes (e/c), Generation (e/c)
+ edges from a8a852e (vertex names):
 [1] Targaryen--Stark       Baratheon--Martell     Baratheon--Stark      
 [4] Martell  --Essos       Martell  --Reach       Martell  --Essos      
 [7] Martell  --Essos       Martell  --Septa       Martell  --Dorne      
[10] Targaryen--Martell     Targaryen--Essos       Targaryen--Essos      
[13] Baratheon--Lannister   Baratheon--Vale        Baratheon--Riverlands 
[16] Baratheon--Crownlands  Baratheon--Reach       Baratheon--Westerlands
[19] Baratheon--Crownlands  Lannister--Lannister   Baratheon--Reach      
[22] Baratheon--Tyrell      Tyrell   --Reach       Tyrell   --Reach      
+ ... omitted several edges

Code

vcount(got_marriages.ig)

[1] 20

Code

ecount(got_marriages.ig)

[1] 255

Code

is_bipartite(got_marriages.ig)

[1] FALSE

Code

is_directed(got_marriages.ig)

[1] FALSE

Code

is_weighted(got_marriages.ig)

[1] FALSE

Code

vertex_attr_names(got_marriages.ig)

[1] "name"

Code

edge_attr_names(got_marriages.ig)

[1] "Type"       "Notes"      "Generation"

Code

table(got_marriages$Type)

 Affair Engaged Married 
     36       2     217 

Code

plot(got_marriages.ig)

Dyad and Triad Census

Now try a full dyad census. This gives us the number of dyads where the relationship is:

• Reciprocal (mutual), or mut
• Asymmetric (non-mutual), or asym, and
• Absent, or null

Now use triad.census in order to do a triad census.

Code

dyad_got = dyad.census(got_marriages.ig)
dyad_got

$mut
[1] 60

$asym
[1] 0

$null
[1] 130

Code

triad_got = triad.census(got_marriages.ig)

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

Code

triad_got

 [1] 625   0 227   0   0   0   0   0   0   0 228   0   0   0   0  60

Global and Local Transitivity or Clustering

Compute global transitivity using transitivity on igraph or gtrans on statnet and local transitivity of specific nodes of your choice, in addition to the average clustering coefficient. What is the distribution of node degree and how does it compare with the distribution of local transitivity?

Code

global_transitivity = transitivity(got_marriages.ig, type = 'global')
global_transitivity

[1] 0.4411765

Code

V(got_marriages.ig)$name

 [1] "Targaryen"   "Baratheon"   "Martell"     "Lannister"   "Tyrell"     
 [6] "Reach"       "North"       "Riverlands"  "Westerlands" "Stark"      
[11] "Vale"        "Arryn"       "Tully"       "Frey"        "Crownlands" 
[16] "Stormlands"  "Essos"       "Septa"       "Dorne"       "Beyond Wall"

Code

V(got_marriages.ig)[c("Targaryen", "Baratheon", "Martell")]

+ 3/20 vertices, named, from a8a852e:
[1] Targaryen Baratheon Martell  

Code

local_transitivity = transitivity(got_marriages.ig, type="local", vids=V(got_marriages.ig)[c("Targaryen", "Baratheon", "Martell")]) 
local_transitivity

[1] 0.3636364 0.4181818 0.4000000

Code

avg_cluster_coef = transitivity(got_marriages.ig, type = 'average')
avg_cluster_coef

[1] 0.5478074

Path Length and Component Structure

Can you compute the average path length and the diameter of the network? Can you find the component structure of the network and identify the cluster membership of each node?

Code

avg_path_length = average.path.length(got_marriages.ig, directed=F)
avg_path_length

[1] 1.9

Code

names(igraph::components(got_marriages.ig))

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

Code

no_compon = igraph::components(got_marriages.ig)$no
no_compon

[1] 1

Code

size_compon = igraph::components(got_marriages.ig)$csize
size_compon

[1] 20