MA7557 Random Graphs and Complex Networks
Complex networks are huge real life networks like Neural, Social, Communication networks or The World wide web. The study of these are hindered by their immense size. The only feasible approaches are studying the local structure or use the idea of random graphs and asymptotes. This course aims to prepare the interested student to delve in to the fascinating area which is a current topic of huge interest.
Introduction to graphs and connectivity,
Complex networks with real world examples: Internet, Social networks, Brain, collaboration network. Scalefreeness and small world properties. Random graphs and the need for it. Useful probabilistic methods and results.
Phase transition in random graphs: The evolution of clusters. The giant component and Central limit theorem. Criticality properties and bounds.
Models suitable for Complex networks with related results:
1. Generalized random graphs,
2. Configuration model
3. Preferential attachment models.
R. van der Hofstad, Random Graphs and complex networks, Vol:1, Cambridge University Press, 2016.
R. van der Hofstad, Random Graphs and complex networks, Vol:1 & 2, (Class notes), 2013-2014, e-copy available from the author.
Prerequisite:Probability basics, familiarity with graphs