Due: Wednesday 09.30.15, 9:00am
All homework is to be completed without assistance from any other student or faculty member. If you need
assistance, please contact Prof. McBride. You must use Mathematica to complete the exploration of the problem
computationally. The write up is to be done in Mathematica as well. Homeworks submitted late incur a 10
percentage point penalty per 24 hours late. Thus, home works submitted after 9:00am Wednesday and by 9:00am
Thursday will be penalized 10 percentage points; from 9:01am Thursday to 9:00am Friday, 20 percentage points,
Last Modified: 2015.09.15
Use of meta-data to analyze relationships is a currently, sometimes hotly, debated topic. Using network analysis of meta-data about relationships between people, interesting patterns can be inferred. In a fun blog post Healy (2013), based in part on work by Han (2009), uses simple
meta-data on membership in organizations in the Boston area in 1775 can identify Paul Revere as a key central figure. Both Han (2009) and
Healy (2013) refer to measures of the centrality of a node in the network. One of the measures they use is the betweenness centrality which
measures the proportion of shortest paths between any two given nodes that a third node lies within.
A separate literature has arisen that uses these same techniques to understand the relationships between co-authors, (e.g. Leskovec, et. al.
(2007)). In the context of co-authors, the question becomes who are the central figures (nodes) in a literature? The pattern of who coauthored with whom reveals information on the centrality of different authors doing research in the literature.
The assignment is going to use data on astrophysics co-authorships from 1995 to 1999 to undertake an analysis of the network relationships
which differs from the typical centrality measures. Instead of betweenness centrality, we’re going to determine hub and authority scores for
each node in the network. Hubs and authorities are generally used as the basis for ranking nodes related to searching for particular nodes and
were proposed by Kleinberg as alternative to Google’s PageRank.
What does all of this have to do with mathematical economics? A graph, or network, is defined by its adjacency matrix. The adjacency
matrix m is a square matrix of dimension n, where n is the number of nodes. The (i, j)th element of the m is equal to one if a link exists from
node i TO node j. Thus, the adjacency matrix need not be symmetric (links between nodes can be directed or undirected). The algorithm for
computing hub and authorities scores for each node is a set of iterated matrix calculations that will converge.
? Research steps to undertake
To undertake the hub and authority analysis, complete the following steps to determine who the most important “hubs” and “authorities” are
in the astrophysics literature:
1. Carefully read sections 14.2 and 14.6.A of Easley and Kleinberg (2010). Read the other parts of the chapter 14 only if you’re interested.
2. Get the ”citations-starting.nb” Mathematica notebook. Setup the Mathematica notebook to pull in the data and create the adjacency
matrix. Instructions are provided in the notebook.
3. Eco414 students: Complete a 4 step (k = 4) hub and authority algorithm using the data provided. Which astrophysicists are the
important hubs or authorities? Interpret what that means.
4. M.A. and 3+1 students: Complete a 4 step (k = 4) hub and authority algorithm using the data provided. This will help you understand
the algorithm. Next, undertake the analysis in the limit as k ‘ 8. Which astrophysicists are the important hubs or authorities? Interpret
what that means.
2 | HW02 – F15.nb
Completing the Assignment
? Document guidelines
Develop a write up of your explorations in an interactive Mathematica notebook that meets professional standards:
The discussion of your computational analysis should be 750-1250 words and the writing should meet professional standards.
The audience for the discussion is other economists who have had training in mathematical economics. Thus, you should use the
language and terminology of mathematical economics to convey your findings.
All sources and direct quotes should be properly cited. Use the APA in-line style for citations in the body of the text and APA style for
listing references at the end of the notebook.
The Mathematica notebook should be well organized into sections with appropriate subsections and discussion of your analysis. Use
appropriate plots and interactive elements to enhance your reader’s comprehension of the discussion.
In the opening section of the notebook, the following statement must be included:
“By submitting the enclosed material, I acknowledged that I did not receive any assistance from any other individual except Prof.
McBride in completing the assignment.”
? Submission guidelines
Name your notebook file ”HW02-uniqueID.nb” where uniqueID is your Miami uniqueID. For example, if I was submitting my file, it
would be named ”HW02-mcbridme.nb”.
Create a pdf version of your notebook file which will be named “HW02-uniqueID.pdf”.
Submit both the .nb and .pdf files via Canvas.
A. Easley, D., Kleinberg, J., 2010. Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge and New
B. Han, S.-K., June 2009. The other ride of paul revere: The brokerage role in the making of the American revolution. Mobilization 14 (2),
C. Healy, K., June 2013. Using metadata to find paul revere.
D. Leskovec, J., Kleinberg, J. and Faloutsos, C. 2007. graph evolution: densification and shrinking diameters. ACM Transactions on
Knowledge Discovery from Data, 1 (1), xx-xx.
As you complete the homework assignment, keep the following grading rubric in mind:
Table 1. Rubric
quality of mathematics
quality of economics
use of Mathematica
quality of written
deep insight into the
deep insight in the
takes full advantage of
with clear, concise
for the issues
for the issues
to the issues
economics are loosely
related to the issues
appropriate use of
standards for clarity
barely uses Mma
for clarity and
or unrelated to issues
economics incorrect or
unrelated to issues
incorrect or improper
use of Mma
fails to meet minimal
for clarity and