My network graph & Choosing Seed Customers for a Referral Campaign

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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':
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##     union

g5 <- graph_from_literal(Jimmy-Mother-Farther-Wife, Jimmy-B:S, Jimmy-A, A-B, Jimmy-G-E, Jimmy-E)

plot(g5)

Interpret your own network according to my tutorial: https://rpubs.com/utjimmyx/networkLinks to an external site.

Answer: Jimmy is the most important person because he has six straight connections. One group is made up of Jimmy, A, and B, and another is made up of Jimmy, G, and E. Jimmy is linked to the chain that leads to Farther and Wife by his mother.

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 and Cara seem to be at the center of things because they are linked to many other people and different parts of the network. Ava, Dan, and Eli, and Cara, Hal, and Ivy, are two groups that are very close to each other. Each group’s members can directly connect with the other two.

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?

With five direct links, Ava has the highest degree and the highest betweenness at 25.83. At 0.050, Brand and Ava are tied for the highest closeness. Because degree counts direct connections, closeness measures distance to others, and betweenness measures how frequently a person lies on the shortest paths between others, the rankings partially agree but vary.

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?)

##ANSWER: I plan on giving Ava and Cara the complimentary samples. With five links and a betweenness of 25.83, Ava has the highest degree. With four connections and a betweenness score of 18.17, Cara comes in second on both categories. Both have the ability to connect multiple parts of the network and directly reach individuals. A high degree does not always indicate a strong bridge,and Kim has higher betweenness than Ivy despite having fewer direct connections.

References:

https://visiblenetworklabs.com/2021/04/16/understanding-network-centrality/Links to an external site.

https://cambridge-intelligence.com/learn/social-network-analysis/Links to an external site.