(CCNSA)

Centre for Advanced Research in Applied Mathematics and Statistics, MAHE, Manipal, India

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.

The objective of the present course is to introduce the science of networks and to study the subfields of the network science which include social network analysis (SNA), collaboration networks (bibliographic citations, product marketing, online social networks), synthetic emergent systems (power grids, the Internet), physical science systems (phase transition, percolation theory, Ising theory), and life science systems (epidemics, metabolic processes, genetics).

**Prerequisite**: Basic understanding of the graphs and probability will be helpful although it is not mandatory

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.

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.

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.

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.

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

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

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 Attackerâ€“Defender Network Risk Problem, Critical Link Analysis, Stability Resilience in Kirchhoff Networks.

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

The course is of 3 credit and the performance of any participant will be continuously evaluated in the tutorials, through submission of assignments, and the delivery of seminars. 100% attendance and aggregate grade point of 5 or above is necessary for the successful completion of the course.

Faculty and Research Scholars of Science, Medicine and Technology having the research interest in the applications of Network Theory, PG and UG students with basic knowledge of graphs and Probability.

Course fee is nil in this academic year. Preference is given to the applicants in the order of faculty members, research scholars and graduate students, as our focus in the present year is to train our in house faculty and build capacity in the subject.

Course fee is nil in this academic year. Preference is given to the applicants in the order of faculty members, research scholars and graduate students, as our focus in the present year is to train our in house faculty and build capacity in the subject.

Start Date | February 09, 2019 |

Day | Every Saturday |

Time | 2.00 pm – 5.00 pm |

Lecture | 1.25 Hrs. |

Tutorials | 1.25 Hrs. |

(Changes in schedule are subject to holidays and availability of resource person.)

Research Interests:
Network Analysis, Graph Theory and its applications, Fuzzy logic and its applications to pattern recognition, Topology , Geometry… Read more

Achievements:
He has more than 250 publications and more than 20 books. Most of these books are prescribed as… Read more

Research Interests:
Generalized Inverse of Matrices and their Applications, Linear Models, Covariance Matrices and Applications, Nonnegative Matrices, Projective Modules and… Read more

Achievements:
He completed his phd in Indian Statistical Institute, Calcutta (July 1993). He has more than 40 publications in… Read more

Research Interests:
Graph Theory, Combinatorics, Linear Algebra, Algebra Read more

Achievements:
He is a Life-time Member of Ramanujan Mathematical Society since 1995. He has given various talks in national… Read more

carams.mahe@gmail.com