Networks Assignment 1: Minimal example solution (R)

### Load standardpackages
library(tidyverse) # Collection of all the good stuff like dplyr, ggplot2 ect.
library(magrittr) # For extra-piping operators (eg. %<>%)

library(tidygraph)
library(igraph)
library(ggraph)

Read Data

el_friendship <- read_delim('https://github.com/SDS-AAU/SDS-master/raw/master/00_data/network_krackhard/Krack-High-Tec-edgelist-Friendship.txt',
                        delim = ' ', col_names = FALSE)
el_advice <- read_delim('https://github.com/SDS-AAU/SDS-master/raw/master/00_data/network_krackhard/Krack-High-Tec-edgelist-Advice.txt',
                        delim = ' ', col_names = FALSE)
el_work <- read_delim('https://github.com/SDS-AAU/SDS-master/raw/master/00_data/network_krackhard/Krack-High-Tec-edgelist-ReportsTo.txt',
                        delim = ' ', col_names = FALSE)

nodes <- read_csv('https://github.com/SDS-AAU/SDS-master/raw/master/00_data/network_krackhard/Krack-High-Tec-Attributes.csv')

Preprocessing

el_friendship %<>%  
  mutate_all(as.numeric) %>%
  filter(X3 == 1) %>%
  select(-X3) %>%
  rename(from = X1, to = X2)

el_advice %<>% 
  mutate_all(as.numeric) %>%
  filter(X3 == 1) %>%
  select(-X3) %>%
  rename(from = X1, to = X2)

el_work %<>% 
  mutate_all(as.numeric) %>%
  filter(X3 == 1) %>%
  select(-X3) %>%
  rename(from = X1, to = X2)

colnames(nodes) <- colnames(nodes) %>% str_to_lower()

nodes %<>%
  rename(name = id) %>%
  mutate(name = name %>% as.character(),
         level = level %>% recode("1" = "ceo", "2" = "vice", "3" = "manager"),
         dept = dept %>% as.character())

1. Create a network

• Generate network objects for the companies organizational structure (reports to), friendship, advice
• This networks are generated from the corresponding edgelists
• Also attach node characteristics from the corresponding nodelist

g_friendship <- el_friendship %>% as_tbl_graph(directed = TRUE) %>%
  left_join(nodes, by = "name")

g_advice <- el_advice %>% as_tbl_graph(directed = TRUE) %>%
  left_join(nodes, by = "name")

g_work <- el_work %>% as_tbl_graph(directed = TRUE) %>%
  left_join(nodes, by = "name")

A: Network level characteristics

Find the overal network level of:

• Density
• Transistivity (Clustering Coefficient)
• Reciprocity

… for the different networks.

nw_stats <- tibble(
  Stat = c('Edge Density', 'Transistivity', 'Reciprocity'),
  Friendship = c(edge_density(g_friendship), transitivity(g_friendship, type ="global"), reciprocity(g_friendship)), 
  Advice = c(edge_density(g_advice), transitivity(g_advice, type ="global"), reciprocity(g_advice)), 
  Work = c(edge_density(g_work), transitivity(g_work, type ="global"), reciprocity(g_work))
  )

Describe and interpret the results. Answer the following questions:

• Are relationships like friendship and advice giving usually reciprocal?
• Are friends of your friends also your friends?
• Are the employees generally more likely to be in a friendship or adviceseeking relationship?

nw_stats

B: Node level characteristics

Likewise, find out:

• Who is most popular in the networks. Who is the most wanted friend, and advice giver? *Are managers in higher hierarchy more popular as friend, and advice giver?

g_friendship <- g_friendship %N>%
  mutate(cent_dgr = centrality_degree(mode = 'in'))

g_advice <- g_advice %N>%
  mutate(cent_dgr = centrality_degree(mode = 'in'))

g_friendship %N>% as_tibble() %>% arrange(desc(cent_dgr)) 

g_advice %N>% as_tibble() %>% arrange(desc(cent_dgr)) 

g_friendship %N>% as_tibble() %>% 
  group_by(level) %>%
  summarise(cent_dgr = cent_dgr %>% mean())

g_advice %N>% as_tibble() %>% 
  group_by(level) %>%
  summarise(cent_dgr = cent_dgr %>% mean())

C: Relational Characteristics

Answer the following questions:

• Are managers from the same 1. department, or on the same 2. hirarchy, 3.age, or 4. tenuere more likely to become friends or give advice? (hint: assortiativity related)
• Are friends more likely to give each others advice?

assortativity_nominal(g_friendship, V(g_friendship)$level %>% factor(), directed = TRUE)

[1] 0.1875

assortativity(g_friendship, V(g_friendship)$age, directed = TRUE)

[1] 0.1002871

assortativity(g_friendship, V(g_friendship)$tenure, directed = TRUE)

[1] -0.09456003

assortativity_nominal(g_advice, V(g_advice)$level %>% factor(), directed = TRUE)

[1] 0.008073818

assortativity(g_advice, V(g_advice)$age, directed = TRUE)

[1] 0.0387598

assortativity(g_advice, V(g_advice)$tenure, directed = TRUE)

[1] 0.1552188

cor(el_friendship_complete %>% pull(X3), 
    el_advice_complete %>% pull(X3))

[1] 0.1743491

3. Aggregated Networks

• Reconstruct the advice and friendship network on the aggregated level of departments, where nodes represent departments and edges the number of cross departmental friendships/advice relationships.

el_friendship_dept <- el_friendship %>% 
  mutate_all(as.character) %>%
  left_join(nodes %>% select(name, dept), by = c('from' = 'name')) %>%
  rename(dept_from = dept) %>%
  left_join(nodes %>% select(name, dept), by = c('to' = 'name')) %>%
  rename(dept_to = dept) %>%
  select(dept_from, dept_to)

g_friendship_dept <- el_friendship_dept %>% as_tbl_graph(directed = TRUE)

el_advice_dept <- el_advice %>% 
  mutate_all(as.character) %>%
  left_join(nodes %>% select(name, dept), by = c('from' = 'name')) %>%
  rename(dept_from = dept) %>%
  left_join(nodes %>% select(name, dept), by = c('to' = 'name')) %>%
  rename(dept_to = dept) %>%
  select(dept_from, dept_to)

g_advice_dept <- el_advice_dept %>% as_tbl_graph(directed = TRUE)

el_work_dept <- el_work %>% 
  mutate_all(as.character) %>%
  left_join(nodes %>% select(name, dept), by = c('from' = 'name')) %>%
  rename(dept_from = dept) %>%
  left_join(nodes %>% select(name, dept), by = c('to' = 'name')) %>%
  rename(dept_to = dept) %>%
  select(dept_from, dept_to)

g_work_dept <- el_work_dept %>% as_tbl_graph(directed = TRUE)

4. Visualization

• Everything goes. Show us some pretty and informative plots.