R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

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(Logan-Mom-Dad, Logan-B:S, Logan-A, A-B, Logan-G-E, Logan-E )

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).

Ava looks the most central visually because she has several direct connections to Ben, Dan, Eli, and Fay. Cara also appears central because she connects the network to Hal and Ivy. Brand is important because it connects Ava, Cara, and Kim.The main cliques are Ava-Dan-Eli, Cara-Hal-Ivy, and Hal-Ivy-Jon. These groups are tightly connected because each person within the group is directly connected to the others.

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

Ava ranks highest in degree centrality with five connections. Cara ranks second with four connections. For closeness centrality, Ava and Brand are tied for the highest score, meaning they can reach the rest of the network efficiently. For the bridge score, Ava ranks highest at 25.83, followed by Cara at 17.67, Brand at 16.50, and Ben at 13.33.The rankings mostly agree because Ava and Cara consistently appear near the top. However, having many connections is not always the same as being a bridge. For example, Hal and Ivy each have three connections, but their bridge scores are much lower because they do not connect as many separate parts of the network.

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 would give the free samples to Ava and Cara. Ava has the highest degree centrality, with five direct connections, and the highest bridge score. This means she can reach many people directly and also acts as an important bridge between different parts of the network.Cara has the second-highest degree and bridge scores. She connects the Brand-Ben area to the group containing Hal, Ivy, and Jon. Choosing Ava and Cara would provide both broad reach and access to multiple network groups. Therefore, having a high degree is not always the same as being a bridge; the bridge score helps identify people who connect separate parts of the network.