Review of Graphs: Graphs and Sub graphs, isomorphism, matrices associated withgraphs, degrees, walks, connected graphs, shortest path algorithm. Eccentricity. 

Connectivity: Graph connectivity, k-connected graphs and blocks. Euler and Hamilton Graphs: Euler graphs, Euler’s theorem. Hamilton cycles, Chinese- postman problem, approximate solutions of traveling salesman problem. Closest neighbour algorithm. Matchings, maximal matchings. Coverings and minimal coverings. Graph Dominations and Independent sets. Vertex colorings, Planar graphs. Euler theorem on planar graphs. 

Large Scale networks: Introduction. Graph and Networks. Network topologies. Examples of large-scale networks and networked systems. Power Law distributions.Scale-free networks.

Random graph models for large networks: Erdos-Renyi graphs, power-law graphs,small world graphs, phase transitions. Network stabilities. 

Graph Networks and Centralities:. Degree and distance centralities. Closeness centrality. Betweeness centrality. Eigenvector centrality and Page ranking algorithmand applications. Clustering coefficient and clustering centrality. Introduction to community detections. 

Case Studies: Transport networks, Biological networks, ect.,

Text books

1. J.A. Bondy and U.S.R. Murty, Graph Theory and Applications, Springer, 2008.
2. Mohammed Zuhair Al-Taie, Seifedine Kadry, Python for Graph and Network
3. Analysis, Springer, 2018.

Reference books

1. Barabasi and Pasfai, Network Science, Cambride University press, 2016.
2. Meghanathan Natarajan, Centrality Metrics for Complext Networks Analysis, IGI publisher, 2018.
3. Networks: An Introduction , M. E. J. Newman , Oxford University Press , 2010.
4. Complex Graphs and Networks , F. Chung and L. Lu , American MathematicalSociety , 2006
5. Graph Algorithms in Neo4j