- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Physics Education Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Graph theoretical methods for understanding student social interactions in physics classrooms

Nathan D. Davis1 and Eric Burkholder1,2

PDF

Phys. Rev. Phys. Educ. Res. 21, 020147 – Published 24 November, 2025

DOI: https://doi.org/10.1103/7jkm-zcmb

Abstract

Social network analysis has become a common methodology within physics education research to quantify the impacts that student interactions and classroom structure have on student outcomes. These relationships are typically quantified using a degree centrality metric based on the number and range of connections a student has, such that a higher degree centrality would indicate a more central position in the network. However, when looking at these interdependent metrics as independent parameters, they do not consistently show any statistically significant relationship with motivational outcomes like self-efficacy or sense of belonging. In this study, we instead characterize students’ network positionality using various “network actor roles” and measure the strength of their connections through network paths, within the context of social capital. In this framing, we are less interested in the impact and importance of individuals than we are in the overall social integration of most students in the class. Using data from an interactive calculus-based physics 1 class, we find that students who are network isolates (no incoming or outgoing connections) or weakly connected report a lower sense of belonging compared with other students, but, consistent with prior research, the number of connections was not correlated with sense of belonging. Similarly, students who were strongly connected to at least one other person reported a higher sense of belonging compared to those who were weakly connected. This indicates the potential for graph theoretical methods to enhance our understanding of student interactions in physics classrooms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. D. Z. Grunspan, B. L. Wiggins, and S. M. Goodreau, Understanding classrooms through social network analysis: A primer for social network analysis in education research, CBE Life Sci. Educ. 13, 167 (2014).
  2. V. Tinto, Stages of student departure: Reflections on the longitudinal character of student leaving, J. Higher Educ. 59, 438 (1988).
  3. V. Tinto, Classrooms as communities: Exploring the educational character of student persistence, J. Higher Educ. 68, 599 (1997).
  4. S. Freeman, S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, H. Jordt, and M. P. Wenderoth, Active learning increases student performance in science, engineering, and mathematics, Proc. Natl. Acad. Sci. U.S.A. 111, 8410 (2014).
  5. E. J. Theobald et al., Active learning narrows achievement gaps for underrepresented students in undergraduate science, technology, engineering, and math, Proc. Natl. Acad. Sci. U.S.A. 117, 6476 (2020).
  6. L. Kramer, E. Fuller, C. Watson, A. Castillo, P. D. Oliva, and G. Potvin, Establishing a new standard of care for calculus using trials with randomized student allocation, Science 381, 995 (2023).
  7. R. R. Hake, Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses, Am. J. Phys. 66, 64 (1998).
  8. L. Deslauriers, E. Schelew, and C. Wieman, Improved learning in a large-enrollment physics class, Science 332, 862 (2011).
  9. J. M. Cámara-Zapata and D. Morales, Cooperative learning, student characteristics, and persistence: An experimental study in an engineering physics course, Eur. J. Eng. Educ. 45, 565 (2020).
  10. J. Pulgar, C. Candia, and P. M. Leonardi, Social networks and academic performance in physics: Undergraduate cooperation enhances ill-structured problem elaboration and inhibits well-structured problem solving, Phys. Rev. Phys. Educ. Res. 16, 010137 (2020).
  11. A. Rezaei, Groupwork in active learning classrooms: Recommendations for users, J. Learn. Spaces 9, 1 (2020), https://libjournal.uncg.edu/jls/article/view/1965.
  12. E. P. Driessen, J. K. Knight, M. K. Smith, and C. J. Ballen, Demystifying the meaning of active learning in postsecondary biology education, CBE Life Sci. Educ. 19, ar52 (2020).
  13. R. A. Lotan, Group-worthy tasks, Educ. Leadership 60, 72 (2003).
  14. R. Dou, E. Brewe, J. P. Zwolak, G. Potvin, E. A. Williams, and L. H. Kramer, Beyond performance metrics: Examining a decrease in students’ physics self-efficacy through a social networks lens, Phys. Rev. Phys. Educ. Res. 12, 020124 (2016).
  15. S. Brin and L. Page, The anatomy of a large-scale hypertextual web search engine, Comput. Networks ISDN Syst. 30, 107 (1998).
  16. S. Fortunato and A. Flammini, Random walks on directed networks: The case of PageRank, Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 2343 (2007).
  17. E. A. Williams, J. P. Zwolak, R. Dou, and E. Brewe, Linking engagement and performance: The social network analysis perspective, Phys. Rev. Phys. Educ. Res. 15, 020150 (2019).
  18. J. P. Zwolak, M. Zwolak, and E. Brewe, Educational commitment and social networking: The power of informal networks, Phys. Rev. Phys. Educ. Res. 14, 010131 (2018).
  19. J. P. Zwolak, R. Dou, E. A. Williams, and E. Brewe, Students’ network integration as a predictor of persistence in introductory physics courses, Phys. Rev. Phys. Educ. Res. 13, 010113 (2017).
  20. R. Dou and J. P. Zwolak, Practitioner’s guide to social network analysis: Examining physics anxiety in an active-learning setting, Phys. Rev. Phys. Educ. Res. 15, 020105 (2019).
  21. P. Bourdieu, The forms of capital, in The Sociology of Economic Life, 3rd ed. (Routledge, New York, NY, 2018).
  22. A. L. Traxler, C. M. D. do Amaral, C. Henderson, E. LaForge, C. Hatcher, M. Swirtz, and R. Barthelemy, Person-centered and qualitative approaches to network analysis in physics education research, Phys. Rev. Phys. Educ. Res. 20, 020132 (2024).
  23. L. S. Vygotsky, Mind in Society (Harvard University Press, London, 2019).
  24. S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, London, 1994).
  25. J. S. Coleman, Social capital in the creation of human capital, Am. J. Sociol. 94, S95 (1988).
  26. J. Coleman, Foundations of Social Theory, 1st ed. (Harvard University Press, Cambridge, MA, 1990).
  27. M. S. Granovetter, The strength of weak ties, in Social Networks (Elsevier, New York, 1977), pp. 347–367.
  28. S. Cwik and C. Singh, Students’ sense of belonging in introductory physics course for bioscience majors predicts their grade, Phys. Rev. Phys. Educ. Res. 18, 010139 (2022).
  29. J. D. Edwards, R. S. Barthelemy, and R. F. Frey, Relationship between course-level social belonging (sense of belonging and belonging uncertainty) and academic performance in general chemistry 1, J. Chem. Educ. 99, 71 (2022).
  30. Y. Li and C. Singh, Sense of belonging is an important predictor of introductory physics students’ academic performance, Phys. Rev. Phys. Educ. Res. 19, 020137 (2023).
  31. E. Burkholder, S. Salehi, S. Sackeyfio, N. Mohamed-Hinds, and C. Wieman, Equitable approach to introductory calculus-based physics courses focused on problem solving, Phys. Rev. Phys. Educ. Res. 18, 020124 (2022).
  32. N. G. Holmes and C. E. Wieman, Introductory physics labs: We can do better, Phys. Today 71, No. 1, 38 (2018).
  33. N. G. Holmes, J. Olsen, J. L. Thomas, and C. E. Wieman, Value added or misattributed? A multi-institution study on the educational benefit of labs for reinforcing physics content, Phys. Rev. Phys. Educ. Res. 13, 010129 (2017).
  34. C. Wieman and N. G. Holmes, Measuring the impact of an instructional laboratory on the learning of introductory physics, Am. J. Phys. 83, 972 (2015).
  35. E. Burkholder, K. Wang, and C. Wieman, Validated diagnostic test for introductory physics course placement, Phys. Rev. Phys. Educ. Res. 17, 010127 (2021).
  36. Y. Li and C. Singh, Inclusive learning environments can improve student learning and motivational beliefs, Phys. Rev. Phys. Educ. Res. 18, 020147 (2022).
  37. PERTS Academic Mindsets Assessment (2020), https://www.perts.net/orientation/ascend.
  38. Y. Li, R. C. Bernardi, and E. Burkholder, The effects of active learning on students’ sense of belonging and academic performance in introductory physics courses, Eur. J. Phys. 45, 045705 (2024).
  39. Y. Li and E. Burkholder, Investigating students’ self-identified and reflected appraisal of femininity, masculinity, and androgyny in introductory physics courses, Phys. Rev. Phys. Educ. Res. 20, 010110 (2024).
  40. J. F. Hair, W. C. Black, B. J. Babin, and R. E. Anderson, Multivariate Data Analysis, 7th ed. (Pearson Education Limited, London, 2014).
  41. G. Csárdi and T. Nepusz, The igraph software package for complex network research, InterJournal 1695, 1 (2006).
  42. M. Bojanowski, intergraph: Coercion Routines for Network Data Objects. R package version 2.0-3, https://mbojan.github.io/intergraph/.
  43. B. R. D. Putnam, Social capital and public life, Am. Prospect. 4, 35 (1993).
  44. C. Goodenow, The psychological sense of school membership among adolescents: Scale development and educational correlates, Psychol. Sch. 30, 79 (1993).
  45. M. I. Suárez, A. R. Dabney, H. C. Waxman, T. P. Scott, and A. O. Bentz, Exploring factors that predict STEM persistence at a large, Public Research University, Int. J. Teach. Learn. Higher Educ. 10, 161 (2021).
  46. M. E. Thompson, Grade expectations: The role of first-year grades in predicting the pursuit of STEM majors for first- and continuing-generation students, J. Higher Educ. 92, 961 (2021).
  47. S. E. Page, The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies, 1st ed. (Princeton Universty Press, Princeton, NJ, 2007).
  48. M. Y. Ahn and H. H. Davis, Sense of belonging as an indicator of social capital, Int. J. Sociol. Soc. Policy 40, 627 (2020).
  49. H. B. Carlone and A. Johnson, Understanding the science experiences of successful women of color: Science identity as an analytic lens, J. Res. Sci. Teach. 44, 1187 (2007).
  50. L. N. Simpendoerfer, M. Sundstrom, M. Dew, and N. G. Holmes, What topics of peer interactions correlate with student performance in physics courses?, Eur. J. Phys. 45, 035704 (2024).

Outline

Information

Phys. Rev. Phys. Educ. Res. 21, 020147– Published 24 November, 2025
  • Received 14 May 2025
  • Accepted 30 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation