Course

Unit I

Graphs and Networks- Review of basic graph theory, Examples of real-world networks, networks and their representation, the adjacency matrix, weighted networks, directed networks, hypergraphs, bipartite networks, trees, planar networks, degree, paths, components, independent paths, connectivity and cut sets, the graph Laplacian, random walks, Properties of Networks.

Unit II

Measures and Metrics: Degree centrality, eigenvector centrality, Katz centrality, page rank, hubs and authorities, closeness centrality, betweenness centrality, groups of vertices, transitivity, reciprocity, signed edges and structural balance, similarity, homophily and assortative mixing.

Unit III

The large-scale structure of Networks, Basic concepts of network communities, community structures, network navigation, Modularity, Girvan-Newman Algorithm, Spectral Bisection Algorithm, Radicchi Edge Clustering Algorithm, Wu-Hubermann Algorithm, Random Walk based Algorithm.

Unit IV

Generalized random graphs, Poisson random graphs- the configuration model, generating functions, power-law degree distribution, Models of Network Growth-Price model, Barabasi & Albert model, other growth models, vertex copying models, Bipartite Network.

Unit V

Processes on Networks: Percolation theory and network resilience, Epidemiological processes, Cascades and information spread, Cohesiveness, Cliques, Clans, Clubs, Plex, Equivalence of ties, Ego-centric networks, Cascade formation and information diffusion in social media. Search on networks, exhaustive network search, guided network search, network navigation; network visualization and semantic zooming, Temporal network, Multilayer networks, Interdependent networks, Controllability of complex networks, Economic and financial network analytics.

The lab experiments/ case studies shall be implemented using any suitable tool such as Python/ R/ MATLAB.

Course Description  

Network science is an evolving field which focuses on the study of patterns of connection in a wide range of physical and social phenomena. The exponential increase in data sets derived from social, economic, and biological networks, along with modern computational power, has increased its relevance. The goal of this course is to provide a mathematical foundation for understanding and analyzing the structure of complex networks. The subject material is interdisciplinary, with topics of graph theory, probability theory, statistical physics, and computer science. 

Course Objectives 

• To understand and explain the workings of systems built upon complex networks  
• To impart fundamental and advanced concepts in the areas of complex networks and network science that focus on study of the models and behavior of networked systems. 

Course Outcomes 

CO-PO Mapping 

Prerequisites  

• Proficiency in programming languages  
• Basic knowledge in graph theory  

1. M.E.J. Newman, “Networks: An Introduction”, Oxford University Press, 2010
2. The structure and function of complex networks. https://epubs.siam.org/doi/10.1137/S003614450342480
3. Statistical mechanics of complex networks, Rev. Mod. Phys., 74(1), 2002.
4. Complex Graphs and Networks, by F. Chung and L. Lu
5. Dougles West, “Introduction to Graph Theory”, Second Edition, PHI Learning Private Limited, 2011.
6. Guido Caldarelli, “Scale-Free Networks”, Oxford University Press, 2007.
7. Alain Barrat, Marc Barthelemy and Alessandro Vespignani, “Dynamical processes on Complex networks”, Cambridge University Press, 2008.
8. Reuven Cohen and Shlomo Havlin, “Complex Networks: Structure, Robustness and Function”, Cambridge University Press, 2010.