Introduction

The purpose of this homework is to familiarize yourself with calculating degree, closeness, and betweenness centrality scores as well as centralization scores for undirected and directed networks in R.

In Parts I and II of this homework we will use two new networks (described below). In Part III, you will use the two networks you created from Homework 1 and Homework 2.


Part I: Working with an Undirected Network

For this part of the homework you will use data from Thomas Grund and James Densley’s study of ties among members of an inner-city gang in London, England. The network is undirected, binary ties collected from anonymized arrests data. We will refer to this network as the LondonGangNet. Note that the object is of class network. To coerce the object to be an object of class matrix, use the as.matrix() function.


For the LondonGangNet network, do the following:

  1. Calculate and report the degree, closeness, and betweenness centrality scores for each actor.
  2. Calculate and report the standardized degree, closeness, and betweenness centrality scores for each actor.
  3. Calculate and report the mean (unstandardized) degree, closeness, and betweenness centrality scores.
  4. Interpret each mean centrality score.
  5. Calculate the graph centralization for degree, closeness, and betweenness centrality.
  6. Interpret each graph centralization score.
  7. Plot the network three times using the gplot() function where each plot sizes the nodes by the centrality score (i.e. a plot for degree centrality, a plot for closeness centrality, and a plot for betweenness centrality).
  8. Examine the plots. Describe how the differences you noted between the centrality measures above are seen in the plots.


Part II: Working with a Directed Network

For this part of the homework you will use data from Mangia Natarajan’s study of a large cocaine trafficking organization in New York City. The network is directed, binary ties of communication between individuals collected from police wiretaps of 151 telephone conversations. We will refer to this network as the CocaineDealingNet. Note that the object is of class network. To coerce the object to be an object of class matrix, use the as.matrix() function.


For the CocaineDealingNet network, do the following:

  1. Calculate and report the indegree, outdegree, closeness, and betweenness centrality scores for each actor.
  2. Calculate and report the standardized indegree, outdegree, closeness, and betweenness centrality scores for each actor.
  3. Calculate and report the mean (unstandardized) indegree, outdegree, closeness, and betweenness centrality score.
  4. Interpret each mean centrality score.
  5. Calculate the graph centralization for indegree, outdegree, closeness, and betweenness centrality.
  6. Interpret each graph centralization score.
  7. Plot the network four times using the gplot() function where each plot sizes the nodes by the centrality score (i.e. a plot for indegree centrality, a plot for outdegree centrality, a plot for closeness centrality, and a plot for betweenness centrality).
  8. Examine the plots. Describe how the differences you noted between the centrality measures above are seen in the plots.


Part III:

Pick one of your networks from Homework 1 and Homework 2 and do the following:

  • If the network is undirected, repeat the steps in Part I.

  • If the network is directed, repeat the steps in Part II.


How to Submit

Download the Homework 3 template prior to beginning. The template contains code for accessing the data files.


Knitting to HTML

When you have completed your homework, click the “Knit” button to render your .RMD file into a .HTML report.


Special Instructions

Upload both your .RMD and .HTML files to the appropriate assignment on the Canvas page for this course. Just click the “Start Assignment” button to upload the files. This assignment is DUE on 2/21.


Before You Submit

Remember to ensure the following before submitting your assignment.

  1. Name your files using this format: Hmwk-##-LastName.rmd and Hmwk-##-LastName.html
  2. Show both the solution for your code and write out your answers in the body text

See Google’s R Style Guide for examples of common conventions.


Common Knitting Issues

.RMD files are knit into .HTML and other formats procedural, or line-by-line.

  • An error in code when knitting will halt the process; error messages will tell you the specific line with the error
  • Certain functions like install.packages() or setwd() are bound to cause errors in knitting
  • Altering a dataset or variable in one chunk will affect their use in all later chunks
  • If an object is “not found”, make sure it was created or loaded with library() in a previous chunk

If All Else Fails: If you cannot determine and fix the errors in a code chunk that’s preventing you from knitting your document, add eval = FALSE inside the brackets of {r} at the beginning of a chunk to ensure that R does not attempt to evaluate it, that is: {r eval = FALSE}. This will prevent an erroneous chunk of code from halting the knitting process.



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