Lab 03 - Degree Centrality - INSTRUCTIONS

CRJ 507 Social Network Analysis

Introduction

The purpose of this lab is to familiarize yourself with calculating degree centrality and degree centralization scores for undirected and directed networks in R. Please review the Degree Centrality chapter of the Social Network Analysis for Crime Analysts textbook and the Degree Centrality and Centralization tutorial in the Social Network Analysis for Crime Analysts using R textbook prior to beginning this lab.

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


Part I: Working with an Undirected Network

For this part of the lab 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 arrest data. This network is available in SNACpack and is called london_gang_net. To review documentation on the network, use ?london_gang_net.

Network and Matrix Objects

Note that the object, and all networks in the SNACpack package, is of class network. This means that to use functions for objects of class matrix (such as dim() or sum()), you need to first coerce the object to a matrix object using as.matrix. For example: my_matrix <- as.matrix( my_network ).


For the london_gang_net network, do the following:

  1. Plot the network using this command: gplot( london_gang_net ).
  2. Describe how you would modify this plot to improve interpretability for a lay audience. Suggest at least three changes and explain why they matter. Be sure to pay attention to the type of network it is and how best to represent the information in the network.
  3. Implement the proposed changes using gplot() and describe how each change affects how we see the network.
  4. Without running any code, describe what kind of actor in this network is likely to have a high degree centrality score.
  5. Calculate the degree centrality score for each actor.
  6. There are three actors with the highest degree centrality scores. Who are they and what does this say about their position in the network?
  7. What does it mean to “standardize” degree centrality? Why might we want to do this?
  8. Calculate the standardized degree centrality scores. Are the three actors with the highest degree centrality scores the same individuals with the highest standardized degree centrality scores? Why or why not?
  9. Calculate the mean degree centrality score. Does the mean degree centrality score represent the “typical” actor in this network? Why or why not?
  10. Graph centralization is often used to assess how “star-like” a network is. What would a completely centralized network look like? What would its degree centrality scores be? Describe it (or, if you are feeling feisty, create one and plot it!).
  11. Calculate the graph centralization score for degree centrality.
  12. Interpret the score. What does it tell us about the distribution of degree centrality scores in the network? Would you describe the network as centralized or decentralized? Justify your answer using both the score and the plot.
  13. Suppose you are an analyst in a gang unit in London. After analyzing this network, what might you do to address gang involvement? How is this informed by your knowledge of the network?


Part II: Working with a Directed Network

For this part of the lab 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 telephone conversations. This network is available in SNACpack and is called cocaine_dealing_net. To review documentation on the network, use ?cocaine_dealing_net.

Network and Matrix Objects

Note that the object, and all networks in the SNACpack package, is of class network. This means that to use functions for objects of class matrix (such as dim() or sum()), you need to first coerce the object to a matrix object using as.matrix. For example: my_matrix <- as.matrix( my_network ).


For the cocaine_dealing_net network, do the following:

  1. Plot the network using this command: gplot( cocaine_dealing_net ).
  2. Describe how you would modify this plot to improve interpretability for a lay audience. Suggest at least three changes and explain why they matter. Be sure to pay attention to the type of network it is and how best to represent the information in the network.
  3. Implement the proposed changes using gplot() and describe how each change affects how we see the network.
  4. Without running any code, describe what kind of actor in this network is likely to have a high indegree centrality score and a high outdegree centrality score. How might that individual be different from someone who has a high indegree centrality score but a low outdegree centrality score? Which one is more prevalent in the network?
  5. Calculate the indegree and outdegree centrality scores for each actor.
  6. There is one actor with the highest outdegree centrality score. What does this say about their position in the network? What behavior or role might explain their high score? (hint: think about what the ties measure).
  7. Calculate the standardized indegree and outdegree centrality scores.
  8. Calculate the mean indegree and outdegree centrality scores. Interpret each mean centrality score and compare them. Is one larger than the other? What does this mean?
  9. Calculate the graph centralization score for indegree and outdegree centrality.
  10. Interpret each score. What does it tell us about the distributions of indegree and outdegree centrality scores in the network? For indegree and outdegree, would you describe the network as centralized or decentralized? Justify your answer using both the score and the plot. Are the scores the same? What does this mean?
  11. Suppose you are an analyst in a drug unit examining cocaine trafficking. After analyzing this network, what might you do to curb cocaine trafficking? How is this informed by your knowledge of the network?


Part III: Your Networks

Pick one of your networks you created in Lab 1 and Lab 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.


Challenge Question

Feeling bold? Try this challenge question. It is not required, but try taking a crack at it.

  • Here is an edgelist for a small 6-node directed network:
    • A → B
    • A → C
    • B → C
    • C → A
    • D → C
    • E → F

Task: Without using a computer, sketch this network.

Then, answer:

  • Which node(s) have the highest indegree?
  • Which node is most central by outdegree?



How to Submit

Download the template for this lab prior to beginning the lab. The template contains code for accessing the data files.


Knitting to HTML

When you have completed your assignment, 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 link for this assignment on the Canvas page for this course.


Before You Submit

Remember to ensure the following before submitting your assignment.

  • Name your files using this format: Lab-##-LastName.rmd and Lab-##-LastName.html
  • 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.


Please report any needed corrections to the Issues page. Thanks!