Course: Complex Networks

Instructor: Dr. Ganesh Bagler

Topics covered in the course:

  1. Introduction to Graph Theory:
    • Introduction to graph theory
    • Examples of graphs
    • Directed and undirected networks
    • Graph theoretical metrics
    • Degree distribution
    • Clustering
    • Adjacency matrix
  2. Classical random graphs:
    • Classical models
    • Loopholes in random graphs
    • Giant component
  3. Small and large worlds:
    • Diameter of the Web
    • Equilibrium versus growing tree
    • Fractal nature of giant connected component
  4. Diversity of networks:
    • Internet
    • World-wide web
    • Cellular networks
    • Co-occurrence networks
  5. Self-organization of networks:
    • Random recursive trees
    • The Barabasi-Albert model
    • General preferential attachment
    • Condensation phenomena
  6. Weighted Networks:
    • The strength of weak ties
    • World-wide airport network
    • Airport network of India
    • Modeling weighted networks
  7. Motifs, cliques, communities:
    • Cliques in networks
    • Statistics of motifs
    • Modularity
    • Detecting communities
    • Hierarchical architecture
  8. Applications of complex networks modeling:
    • Examples of real-world networks
    • Application for biological systems modeling

Reference book:

  1. "Lectures on Complex Networks" by SN Dorogovtsev (Oxford University Press)
  2. "The structure of complex networks" by Ernesto Estrada