R Markdown

This is an R Markdown document. We will use network analysis to understand how people are connected and how businesses can identify influential customers for marketing campaigns.

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(
  X-Mom-Dad-Wife,
  X-Wife,
  Wife-Mom,
  X-B:S,
  X-A,
  A-B,
  X-G-E,
  X-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,
  Brand-Cara,
  Ava-Dan:Eli:Fay,
  Ben-Gus,
  Cara-Hal:Ivy,
  Dan-Eli,
  Fay-Gus,
  Hal-Ivy-Jon,
  Brand-Kim-Jon
)

set.seed(123)

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:

I think Ava and Brand appear to be the most central because they connect with different people throughout the network. Ava has connections with several people, while Brand helps connect other groups. Some tightly connected groups include Ava, Dan, and Eli, as well as Cara, Hal, and Ivy.

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 has the highest degree with 5 connections and the highest betweenness at 25.83. Ava and Brand are tied for the highest closeness at 0.050. Cara is also important because she ranks second in betweenness. The rankings are not completely the same because having more connections does not always mean someone is the best at connecting different groups.

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?)

Your answer:

I would choose Ava and Cara to receive the free samples. Ava has the highest degree with 5 connections and the highest betweenness at 25.83, meaning she can reach many people and help connect different groups. Cara would be my second choice because she has 4 connections and a betweenness score of 18.17. I think both would be good choices because they can help spread information about the product to different people through social media.

References

Visible Network Labs. Understanding network centrality.

https://visiblenetworklabs.com/2021/04/16/understanding-network-centrality/

Cambridge Intelligence. Social network analysis.

https://cambridge-intelligence.com/learn/social-network-analysis/