Certificate Course on Network Science and its Applications
(CCNSA)

Network science, or the science of networks, is the study of the theoretical foundations of network structure/dynamic behavior and the application of networks to many sub fields.

Unit 1:  (3 sessions)

Introduction to Network Science and its characteristics – Basics of probability: Definition, properties, conditional probability, random variables and some important distributions – Basics of graphs, characteristics and parameters, types of graphs – Matrices associated with graphs – Spectral properties of graphs – Problems and solutions related to networks, using programming.

Unit 2:  (3 sessions)

Random networks: generation, degree distributions, entropy, properties and analysis, average path length, cluster coefficient and link efficiency – Properties: Diameter, radius – Closeness calculation – Weak ties in random network – Randomization and analysis.

Small world networks: Generation of SWNs, Watts-Strogatz (WS) procedure, degree sequences of SWNs – Properties of SWNs: Entropy vs. Rewiring Probability, Entropy vs. Density, Path length of SWN, Cluster coefficient of SWN, Closeness in SWNs – Path length and fact transition – Navigating small worlds – Weak ties in SWNs.

Unit 3:  (2 sessions)

Scale free networks: Generating scale free networks, Barabasi-Albert network – Scale free network power law – Properties of scale free network: Hub degree vs. density, average path length, closeness, cluster coefficient – Navigation in SFNs: Maximum degree navigation vs. density, Maximum degree navigation vs. Hub degree, Weak ties in scale-free Pointville, and analysis of path length and communication, cluster coefficient, Hub degree.

Network emergence: Open loop emergence, feedback loop emergence. Emergence in different branches of science: Social science, physical science, and biology – Genetic evolution: Hub emergence, cluster emergence – Designer network: Degree sequence emergence, generating networks with given degree sequence – Permutation network emergence – Applications of emergence.

Unit 4:  (2 sessions)

Epidemics models: Kermack-McKendrick model, Epidemic thresholds, SIR model, peak infection density in structured networks, SIS epidemics – Persistent epidemic in the network – Random network epidemic threshold, epidemic threshold in general network, fixed point infection density – Epidemic simulation – Counter measures algorithm – Counter measure seeding strategies, antigen simulation.

Unit 5:  (2 sessions)

Network Risk – Critical Node Analysis – Game Theory Considerations – The General Attacker–Defender Network Risk Problem – Critical Link Analysis – Stability Resilience in Kirchhoff Networks.

Static Models in Biology – Dynamic Analysis – Protein Expression Networks – Mass Kinetics Modeling.

Seminars may be chosen from the following topics:

Synchrony: A Cricket Social Network, Kirchhoff Networks, Pointville Electric Power Grid

Influence Networks: Anatomy of Buzz, Power in Social Networks, Conflict in I-Nets, Command Hierarchies, Emergent Power in I-Nets

Vulnerability: Network Risk, Critical Node Analysis, Game Theory Considerations, The General Attacker–Defender Network Risk Problem, Critical Link Analysis, Stability Resilience in Kirchhoff Networks.

Text books & References:

1. Bapat RB. Graphs and matrices. New York: Springer; 2010.
2. Deo N. Graph theory with applications to engineering and computer science. Courier Dover Publications; 2017.
3. Lewis TG. Network Science: Theory and applications. John Wiley & Sons; 2011.
4. Newman M. Networks. Oxford university press; 2018.
5. Ramachandran S, Arumugam S. Invitation to graph theory. Scitech publication pvt. Ltd, Reprint. 2009.