Ranking Academic Advisors: Analyzing Scientific Advising Impact Using MathGenealogy Social Network

  • Alexander Semenov
  • Alexander Veremyev
  • Alexander Nikolaev
  • Eduardo L. Pasiliao
  • Vladimir BoginskiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11280)


Advising and mentoring Ph.D. students is an increasingly important aspect of the academic profession. We define and interpret a family of metrics (collectively referred to as “a-indices”) that can be applied to “ranking academic advisors” using the academic genealogical records of scientists, with the emphasis on taking into account not only the number of students advised by an individual, but also subsequent academic advising records of those students. We also define and calculate the extensions of the proposed indices that account for student co-advising (referred to as “adjusted a-indices”). Finally, we extend the proposed metrics to ranking universities and countries with respect to their “collective” advising impacts. To illustrate the proposed metrics, we consider the social network of over 200,000 mathematicians (as of July 2018) constructed using the Mathematics Genealogy Project data: the network nodes represent the mathematicians who have completed Ph.D. degrees, and the directed edges connect advisors with their students.


Social networks Big data Scientific advising impact a-indices Mathematics genealogy project 



Work of A. Semenov was funded in part by the AFRL European Office of Aerospace Research and Development (grant no. FA9550-17-1-0030). This material is based upon work supported by the AFRL Mathematical Modeling and Optimization Institute.


  1. 1.
    Arslan, E., Gunes, M.H., Yuksel, M.: Analysis of academic ties: a case study of mathematics genealogy. In: GLOBECOM Workshops (GC Wkshps), pp. 125–129. IEEE (2011)Google Scholar
  2. 2.
    Boldi, P., Vigna, S.: Axioms for centrality. Internet Math. 10(3–4), 222–262 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Broido, A.D., Clauset, A.: Scale-free networks are rare (2018). arXiv preprint arXiv:1801.03400
  4. 4.
    Gargiulo, F., Caen, A., Lambiotte, R., Carletti, T.: The classical origin of modern mathematics. EPJ Data Sci. 5(1), 26 (2016)CrossRefGoogle Scholar
  5. 5.
    Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2010)zbMATHGoogle Scholar
  6. 6.
    Malmgren, R.D., Ottino, J.M., Amaral, L.A.N.: The role of mentorship in protégé performance. Nature 465(7298), 622 (2010)CrossRefGoogle Scholar
  7. 7.
    Marchiori, M., Latora, V.: Harmony in the small-world. Phys. A: Stat. Mech. Appl. 285(3–4), 539–546 (2000)CrossRefGoogle Scholar
  8. 8.
    Myers, S.A., Mucha, P.J., Porter, M.A.: Mathematical genealogy and department prestige. Chaos Interdiscip. J. Nonlinear Sci. 21(4), 041104 (2011)CrossRefGoogle Scholar
  9. 9.
    Rossi, L., Freire, I.L., Mena-Chalco, J.P.: Genealogical index: a metric to analyze advisor-advisee relationships. J. Inf. 11(2), 564–582 (2017)Google Scholar
  10. 10.
    Taylor, D., Myers, S.A., Clauset, A., Porter, M.A., Mucha, P.J.: Eigenvector-based centrality measures for temporal networks. Multiscale Model. Simul. 15(1), 537–574 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Tsakas, N.: On decay centrality. BE J. Theor. Econ. (2016)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alexander Semenov
    • 1
  • Alexander Veremyev
    • 2
  • Alexander Nikolaev
    • 3
  • Eduardo L. Pasiliao
    • 4
  • Vladimir Boginski
    • 2
    Email author
  1. 1.University of Jyvaskyla, Faculty of Information TechnologyUniversity of JyvaskylaFinland
  2. 2.University of Central FloridaOrlandoUSA
  3. 3.University at BuffaloBuffaloUSA
  4. 4.Air Force Research Laboratory, Eglin AFBNicevilleUSA

Personalised recommendations