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library(igraph)
## 
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union
g5 <- graph_from_literal(Mom-Dad,Abigayl-Mom, Mom-Dad-Abigayl, Mom-Dad-Gilbert, Mom-Dad-Ernan-Sophie:Audrey:EJ:Brenda, Mom-Dad-Nathan, Mom-Dad-Marcos-Rey, Mom-Dad-Emily-Noah )

plot(g5)

Scenario

A fitness-apparel brand is launching a new product and can give free samples to only two people. The network below shows who influences whom on social media. Use network metrics to decide who should receive the samples.

library(igraph)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:igraph':
## 
##     as_data_frame, groups, union
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
# A social media network around a brand
g_mkt <- graph_from_literal(
  Brand-Ava-Ben-Cara,       # chain of connections
  Brand-Cara,
  Ava-Dan:Eli:Fay,          # Ava is connected to Dan, Eli, and Fay
  Ben-Gus,
  Cara-Hal:Ivy,
  Dan-Eli,
  Fay-Gus,
  Hal-Ivy-Jon,
  Brand-Kim-Jon
)

set.seed(123)  # fixes the layout so the plot looks the same each time
plot(g_mkt, vertex.color = "lightblue", vertex.label.color = "black")

Tasks

Task 1: Visualize the network

Look at the plot above. Who looks most “central” visually? Identify any cliques (tightly connected groups).

Your answer: Visually Brand and Ben are more central, but Ava is the most connected because she has 5 lines tying her to Eli,Dan,Fay,Ben,and Brand.The 2 cliques that are in the graph are Hal,Ivy,and Cara. The other clique is Ava,Eli,and Dan.

Task 2: Compare centrality measures

Compute degree, closeness, and betweenness, then put the results in one data frame and rank the nodes.

centrality_df <- data.frame(
  person      = V(g_mkt)$name,
  degree      = degree(g_mkt),
  closeness   = round(closeness(g_mkt), 3),
  betweenness = round(betweenness(g_mkt), 2)
)
centrality_df %>% arrange(desc(betweenness))
##       person degree closeness betweenness
## Ava      Ava      5     0.050       25.83
## Cara    Cara      4     0.048       18.17
## Brand  Brand      3     0.050       17.00
## Ben      Ben      3     0.048       13.33
## Kim      Kim      2     0.037        5.00
## Ivy      Ivy      3     0.037        4.50
## Fay      Fay      2     0.036        2.17
## Gus      Gus      2     0.034        1.50
## Jon      Jon      2     0.033        1.50
## Dan      Dan      2     0.034        0.00
## Eli      Eli      2     0.034        0.00
## Hal      Hal      2     0.034        0.00

Your answer: Which people rank highest on each measure? Do the rankings agree? Ava ranks the highest on all the measures. The rankings slightly agree since there is a closeness between Ava,Cara,Brand,and Ben. There is a clear divide between the other people and it makes the bridges harder to connect to one another.

Task 3: Choose two seed customers

Which two people should receive free samples? Justify your choice using at least two different metrics. (Hint: is high degree the same as being a bridge?)

-I think that the 2 people who should get the free samples should be Ava and Cara. I made this decision based on the fact that Ava is chosen for degree and closeness and Cara is chosen for betweenness