### Instructor: Dr. Ganesh Bagler

### Topics covered in the course:

- Introduction to Graph Theory:
- Introduction to graph theory
- Examples of graphs
- Directed and undirected networks
- Graph theoretical metrics
- Degree distribution
- Clustering
- Adjacency matrix

- Classical random graphs:
- Classical models
- Loopholes in random graphs
- Giant component
- Small and large worlds:
- Diameter of the Web
- Equilibrium versus growing tree
- Fractal nature of giant connected component
- Diversity of networks:
- Internet
- World-wide web
- Cellular networks
- Co-occurrence networks
- Self-organization of networks:
- Random recursive trees
- The Barabasi-Albert model
- General preferential attachment
- Condensation phenomena
- Weighted Networks:
- The strength of weak ties
- World-wide airport network
- Airport network of India
- Modeling weighted networks
- Motifs, cliques, communities:
- Cliques in networks
- Statistics of motifs
- Modularity
- Detecting communities
- Hierarchical architecture
- Applications of complex networks modeling:
- Examples of real-world networks
- Application for biological systems modeling

### Reference book:

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