2014 ICM Problem： Using Networks to Measure Influence and Impact
One of the techniques to determine influence of academic research is to build and measure properties of citation or coauthor networks. Coauthoring a manuscript usually connotes a strong influential connection between researchers. One of the most famous academic coauthors was the 20thcentury mathematician Paul Erdös who had over 500 coauthors and published over 1400 technical research papers. It is ironic, or perhaps not, that Erdös is also one of the influencers in building the foundation for the emerging interdisciplinary science of networks, particularly, through his publication with Alfred Rényi of the paper “On Random Graphs” in 1959. Erdös’s role as a collaborator was so significant in the field of mathematics that mathematicians often measure their closeness to Erdös through analysis of Erdös’s amazingly large and robust coauthor network (see the website http://www.oakland.edu/enp/ ). The unusual and fascinating story of Paul Erdös as a gifted mathematician, talented problem solver, and master collaborator is provided in many books and online websites
(e.g., http://wwwhistory.mcs.stand.ac.uk/Biographies/Erdos.html). Perhaps his itinerant lifestyle, frequently staying with or residing with his collaborators, and giving much of his money to students as prizes for solving problems, enabled his coauthorships to flourish and helped build his astounding network of influence in several areas of mathematics.
In order to measure such influence as Erdös produced, there are networkbased evaluation tools that use coauthor and citation data to determine impact factor of researchers, publications, and journals. Some of these are Science Citation Index, H factor, Impact factor, Eigenfactor, etc. Google Scholar is also a good data tool to use for network influence or impact data collection and analysis. Your team’s goal for ICM 2014 is to analyze influence and impact in research networks and other areas of society. Your tasks to do this include:
1) Build the coauthor network of the Erdos1 authors (you can use the file from the website https://files.oakland.edu/users/grossman/enp/Erdos1.html or the one we include at Erdos1.htm ). You should build a coauthor network of the approximately 510 researchers from the file Erdos1, who coauthored a paper with Erdös, but do not include Erdös. This will take some skilled data extraction and modeling efforts to obtain the correct set of nodes (the Erdös coauthors) and their links (connections with one another as coauthors). There are over 18,000 lines of raw data in Erdos1 file, but many of them will not be used since they are links to people outside the Erdos1 network. If necessary, you can limit the size of your network to analyze in order to calibrate your influence measurement algorithm. Once built, analyze the properties of this network. (Again, do not include Erdös  he is the most influential and would be connected to all nodes in the network. In this case, it’s coauthorship with him that builds the network, but he is not part of the network or the analysis.)

2) Develop influence measure(s) to determine who in this Erdos1 network has significant influence within the network. Consider who has published important works or connects important researchers within Erdos1. Again, assume Erdös is not there to play these roles.

3) Another type of influence measure might be to compare the significance of a research paper by analyzing the important works that follow from its publication. Choose some set of foundational papers in the emerging field of network science either from the attached list (NetSciFoundation.pdf) or papers you discover. Use these papers to analyze and develop a model to determine their relative influence. Build the influence (coauthor or citation) networks and calculate appropriate measures for your analysis. Which of the papers in your set do you consider is the most influential in network science and why? Is there a similar way to determine the role or influence measure of an individual network researcher? Consider how you would measure the role, influence, or impact of a specific university, department, or a journal in network science? Discuss methodology to develop such measures and the data that would need to be collected.

4) Implement your algorithm on a completely different set of network influence data  for instance, influential songwriters, music bands, performers, movie actors, directors, movies, TV shows, columnists, journalists, newspapers, magazines, novelists, novels, bloggers, tweeters, or any data set you care to analyze. You may wish to restrict the network to a specific genre or geographic location or predetermined size.

5) Finally, discuss the science, understanding and utility of modeling influence and impact within networks. Could individuals, organizations, nations, and society use influence methodology to improve relationships, conduct business, and make wise decisions? For instance, at the individual level, describe how you could use your measures and algorithms to choose who to try to coauthor with in order to boost your mathematical influence as rapidly as possible. Or how can you use your models and results to help decide on a graduate school or thesis advisor to select for your future academic work?

6) Write a report explaining your modeling methodology, your networkbased influence and impact measures, and your progress and results for the previous five tasks. The report must not exceed 20 pages (not including your summary sheet) and should present solid analysis of your network data; strengths, weaknesses, and sensitivity of your methodology; and the power of modeling these phenomena using network science.
*Your submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.