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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(GENESIS-CHARLIE,LAURA-GENESIS,BRYAN-GENESIS,GENESIS-MARKOS,GENESIS-CARLOS,GENESIS-AMINA,AMINA-CARLOS,CARLOS-AMELIA,AMELIA-AMAEYA)
plot(g5,vertex.color = "purple",vertex.size = 35,vertex.label.cex = 1.1,main = "My Family Network")

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 = "purple", vertex.label.color = "red")

Tasks

Task 1: Visualize the network

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

Your answer:

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? In my family network, GENESIS ranks highest in degree centrality because she has the most direct connections to other family members. She is connected to CHARLIE, LAURA, MARKOS, BRYAN, and CARLOS. GENESIS also ranks highest in closeness centrality because she can reach every other person in the network through the fewest steps. ## Task 3: Choose two seed customers I would choose GENESIS and CHARLIE to receive the free samples. DIANE should receive a sample because she has the highest degree centrality and betweenness centrality. She has the most direct connections and acts as the bridge between different parts of the family network. LAURA would be my second choice because she is connected to both JUAN and DIANE, giving her greater reach than CHARLIE, LAURA, or MARKOS She can help spread information through another branch of the network. 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?)