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Mathematical Foundations and Basic Theorizing


A survey of key relational, graph-theoretic and algebraic ideas. This will be the only class that is largely mathematical. However, the math is extremely easy -- really just a bunch of simple definitions. We also discuss a set of well-known network theories in order to see how they make use of fundamental concepts.

 

Topics

  • Relations

  • Graphs

  • Matrices

Readings

  • S.P. Borgatti. 2004. Introduction to Graph Theory. [pdf]
  • Granovetter, M. 1973. The strength of weak ties. American Journal of Sociology, Vol. 78, No. 6. pp. 1360-1380. [^pdf] (focus on first 10 pages: pp 1360-1369).
  • Burt, R. The social structure of social capital. [pdf]
  • Borgatti, S. P. 1997. Structural holes: Unpacking Burt’s redundancy measures. Connections, 20(1): 35‑38. [pdf]
  • Krackhardt & Carley. 1998. A PCANS Model of Structure in Organizations." Proceedings of the 1998 International Symposium on Command and Control Research and Technology. June. Monterey, CA. [pdf]

Additional

  • Carter et al. Linear Algebra. Excellent online introduction to matrices [html]
  • Wikipedia on relational composition [html]
  

Exercises

Slides

 

Handouts

 

Bibliography

 

Management Literature

  • Krackhardt, D. 1994. Graph Theoretical Dimensions of Informal Organizations." In Kathleen Carley & Michael Prietula (eds.), Computational Organizational Theory. Hillsdale, NJ: Lawrence Erlbaum Associaties, Inc. pp. 89-111. [pdf]

  • Lincoln, J.R. 1982. Intra (and inter-) organizational networks. Research in the sociology of organizations 1:1-38.

  • Tichy, N. M., M. L. Tushman, and C. Fombrun, "Social Network Analysis for Organizations", Academy of Management Review, Vol. 4, No. 4, 1979, pp. 507-519 [^pdf]

Mathematical

  • Harary, Frank & R. Z. Norman (1953) Graph Theory as a Mathematical Model in Social Science. Ann Arbor: University of Michigan.

  • Harary, Frank, R.Z. Norman & D. Cartwright (1965) Structural Models: An Introduction to the Theory of Directed Graphs. New York: John Wiley & Sons.

  • Harary, Frank (1969) Graph Theory. Reading, MA: Addison Wesley.

  • Hage, Per (1979) Graph theory as a structural model in cultural anthropology. Annual Review of Anthropology, 8 : 115-136.

  • Hage, Per & Frank Harary (1983) Structural Models in Anthropology.Cambridge: Cambridge University.

Backcloth and Traffic

  • Guetzkow, H.,& Simon, H. A. (1955). The impact of certain communication nets upon organization and performance in task-oriented groups. Management Science, 1, 233-250.

 

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