Week 2 Challenge

challenge_2

Ananya Pujary

Describing the Basic Structure of a Network

Author

Ananya Pujary

Published

February 22, 2023

Challenge Overview

Describe the basic structure of a network following the steps in tutorial of week 2, this time using a dataset of your choice: for instance, you could use Marriages in Game of Thrones or Like/Dislike from week 1.

Another more complex option is the newly added dataset of the US input-output table of direct requirements by industry, available in the Bureau of Economic Analysis. Input-output tables show the economic transactions between industries of an economy and thus can be understood as a directed adjacency matrix. Data is provided in the form of an XLSX file, so using read_xlsx from package readxl is recommended, including the sheet as an argument (2012 for instance).

Identify and describe content of nodes and links, and identify format of data set (i.e., matrix or edgelist, directed or not, weighted or not), and whether attribute data are present. Be sure to provide information about network size (e.g., information obtained from network description using week 1 network basic tutorial commands.)

Describe the Network Data

Listing objects

Code

# listing all objects
ls()

character(0)

I’ll be working with the Game of Thrones like-dislike dataset.

Code

got_marriages<-read_csv("../posts/_data/got/got_marriages.csv")

Rows: 255 Columns: 5
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (5): From, To, Type, Notes, Generation

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

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

Code

got_marriages.ig <-graph_from_data_frame(got_marriages, directed = FALSE)

Network Size and Features

Code

# network size
vcount(got_marriages.ig)

[1] 20

Code

ecount(got_marriages.ig)

[1] 255

Code

# network features
is_directed(got_marriages.ig)

[1] FALSE

Code

is_bipartite(got_marriages.ig)

[1] FALSE

Code

is_weighted(got_marriages.ig)

[1] FALSE

This network has 20 vertices and 255 edges. It is not directed, not bipartite, and not weighted.

Network Attributes

Listing the vertex and edge attributes:

Code

vertex_attr_names(got_marriages.ig)

[1] "name"

Code

edge_attr_names(got_marriages.ig)

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

Dyad and Triad Census

Now, trying a dyad census to figure out the number of dyads that have reciprocal, asymmetric, and absent relationships:

Code

igraph::dyad.census(got_marriages.ig)

$mut
[1] 60

$asym
[1] 0

$null
[1] 130

In this network, there are 60 mutual, 0 asymmetric, and 130 absent relationships. This is interesting since it maps marriages connections in the GOT universe, indicating that a lot of characters aren’t married, and there are no asymmetric ties because marriage is a mutual partnership.

Now doing a triad census:

Code

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.

 [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 clustering
igraph::transitivity(got_marriages.ig, type="global")

[1] 0.4411765

Code

# local clustering
transitivity(got_marriages.ig, type="average")

[1] 0.5478074

Code

# listing vertices I'm interested in
V(got_marriages.ig)[V(got_marriages.ig)$name == "Lannister"]

+ 1/20 vertex, named, from 7c2b352:
[1] Lannister

Code

# checking ego network transitivity
igraph::transitivity(got_marriages.ig, type="local", vids=V(got_marriages.ig)$name)

 [1] 0.3636364 0.4181818 0.4000000 0.7000000 1.0000000 0.3636364 0.1666667
 [8] 0.5714286 0.6666667 0.4166667 0.4666667 0.6666667 0.5000000 0.2888889
[15] 0.5714286 0.7000000 0.6000000       NaN 1.0000000       NaN

Code

igraph::transitivity(got_marriages.ig, type="local", vids=V(got_marriages.ig)[c("Targaryen","Baratheon", "Lannister")])

[1] 0.3636364 0.4181818 0.7000000

Code

# trans.vector <- transitivity(like_dislike.ig, type = "local")
# trans.vector[V(like_dislike.ig)$name == "Jon Snow"]

The global transitivity is 0.4411765 and the local transitivity is 0.5478074 The local transitivity of “Targaryen” is 0.3636364, 0.4181818 for “Baratheon”, and 0.7000000 for “Lannister”. Thus, Lannister seems to be the family with the most marriages when compared to Targaryen and Baratheon.

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

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

[1] 1.9

Code

# diameter of network
diameter(got_marriages.ig, directed=FALSE)

[1] 4

Code

# looking at the network component structure
names(igraph::components(got_marriages.ig))

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

Code

## number of components
igraph::components(got_marriages.ig)$no

[1] 1

Code

## size of each component
igraph::components(got_marriages.ig)$csize

[1] 20

Code

# calculate distance using unweighted edges
distances(got_marriages.ig,"Lannister","North", weights=NA)

          North
Lannister     2

The average path length is 1.9 and the diameter is 4, which indicates that it is a relatively small network. It has one component with 20 nodes, so it is very connected. The distance between North and Lannister is 2, which is around the average path length.

Code

# plotting the network
E(got_marriages.ig)$color <- colorRampPalette(c("yellow", "blue"))(11)[E(got_marriages.ig)$weight + 6]

Warning in length(eattrs[[name]]) <- ec: length of NULL cannot be changed

Code

V(got_marriages.ig)$color[grep("Lannister", V(got_marriages.ig)$name)] <- "red"

plot(got_marriages.ig)