Graph Theory

In this class we covered the basics of Graph theory and introduced some of it's fundamental concepts:

  • Adjacency Matrix
  • Degree Distribution
  • Paths and Cycles
  • Clustering Coefficient
  • Network Diameter
As an application of some of these concepts, and as a way of showing their relevance in a practical application, we analyzed the Watts and Strogatz Small World network.

References:

  1. E. Estrada, D. J. Higam, "Network properties Revealed through Matrix Functions", SIAM Review 52, 696 (2010)
  2. E. W. Dijkstra, "A note on two problems in connexion with graphs", Numerische Mathematik 1, 269 (1959)
  3. J. Travers, S. Milgram, "An Experimental Study of the Small World Problem", Sociometry 32, 425 (1969)
  4. D. Watts, S. Strogatz, "Collective dynamics of 'small-world' networks", Nature 393, 440 (1998)

Lecture Notes

Lecture 1 - Graph Theory
Jan 31, 2011