, Volume 99, Issue 3, pp 973–998 | Cite as

Evolutionary events in a mathematical sciences research collaboration network

  • Jason Cory Brunson
  • Steve Fassino
  • Antonio McInnes
  • Monisha Narayan
  • Brianna Richardson
  • Christopher Franck
  • Patrick Ion
  • Reinhard LaubenbacherEmail author


This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985–2009. Rather than modeling the network cumulatively, this study traces the evolution of the “here and now” using fixed-duration sliding windows. The analysis uses a suite of common network diagnostics, including the distributions of degrees, distances, and clustering, to track network structure. Several random models that call these diagnostics as parameters help tease them apart as factors from the values of others. Some behaviors are consistent over the entire interval, but most diagnostics indicate that the network’s structural evolution is dominated by occasional dramatic shifts in otherwise steady trends. These behaviors are not distributed evenly across the network; stark differences in evolution can be observed between two major subnetworks, loosely thought of as “pure” and “applied”, which approximately partition the aggregate. The paper characterizes two major events along the mathematics network trajectory and discusses possible explanatory factors.


Mathematics research Collaboration networks Evolving networks 

Mathematics Subject Classification

91D30 05C82 



The authors are grateful to the American Mathematical Society for providing access to the MR database and for agreeing to make the data publicly available (by request to the Executive Director). The authors thank Sastry Pantula and Philippe Tondeur for helpful information, and Sid Redner, Betsy Williams, and participants of the Summer 2010 REU in Modeling and Simulation in Systems Biology for helpful conversations and support. J. C. Brunson, S. Fassino, A. McInnes, M. Narayan, and B. Richardson were partially funded by NSF Award:477855. A. McInnes and B. Richardson were partially funded by HHMI:52006309. S. Fassino, A. McInnes, M. Narayan, and B. Richardson contributed equally.

Supplementary material

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  • Jason Cory Brunson
    • 1
  • Steve Fassino
    • 2
  • Antonio McInnes
    • 3
  • Monisha Narayan
    • 4
  • Brianna Richardson
    • 3
  • Christopher Franck
    • 5
  • Patrick Ion
    • 6
  • Reinhard Laubenbacher
    • 7
    Email author
  1. 1.Virginia Bioinformatics InstituteBlacksburgUSA
  2. 2.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  3. 3.Department of Mathematics and Computer ScienceOakwood UniversityHuntsvilleUSA
  4. 4.Lyman Briggs CollegeMichigan State UniversityEast LansingUSA
  5. 5.Laboratory for Interdisciplinary Statistical AnalysisBlacksburgUSA
  6. 6.Mathematical ReviewsAnn ArborUSA
  7. 7.Center for Quantitative MedicineUniversity of Connecticut Health CenterFarmingtonUSA

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