###### CR15 Master 2 course organised by

- ENS Lyon Computer Science Department
- IXXI – Rhone Alpes Complex System Institute

**24 hours lecture + 6 hours tutorial (4 ECTS)**

###### Lecturers:

**Márton KARSAI** – marton.karsai@ens-lyon.fr

Office: ENS Lyon, IXXI, site Monod, N222

Tel: +33 426 233 805

Web: perso.ens-lyon.fr/marton.karsai

**Eric FLEURY** – eric.fleury@ens-lyon.fr

Office: ENS Lyon, IXXI, site Monod, N232

###### Tutorials:

**Samuel UNICOMB** – samuel.unicomb@ens-lyon.fr

###### Materials:

The course consists of two parts. The first part is concentrating on the related theories, algorithms, models and measures of networks, while the second part gives an introduction to the different types, representations, and applications of complex networks.

Tutorial is given in parallel to the course where the related analytic calculations and network implementations will be discussed. Tutorial is not mandatory for students out of the Modeling Complex Systems M2 program.

The course is mandatory for students in the Modeling Complex Systems M2 program and included in the course offer for M2 Computer Science students at ENS Lyon. Students from other master programs are also welcome.

Prerequisites: Background in graph theory, statistical analysis, and computer algorithms is an advantage but is not mandatory, as the course intends to be accessible for students coming from different disciplines

Evaluation: Attendants will complete course work during the tutorial and will need to pass a written exam in the end of the course.

When: September 2017 – January 2018

###### Subjects:

**Introduction and general network characteristics**(MK)- Complex systems as complex networks
- Representation of complex networks
- Characteristic measures of complex networks

**Centrality measures**(EF)- Betweenness centrality
- Katz centrality
- Page-rank centrality

**Network similarity measures**(EF)- Source of similarity
- Similarity measures

**Characterising heterogenous distributions**(EF)- Characters of scale-free distributions
- Fitting scale-free distributions

**Erdös-Rényi random networks**(EF)- Definitions and statistical properties
- Structural phase transition

**Configuration model networks**(EF)- Definitions and statistical properties
- Stochastic block models

**Small-world property, Watt-Strogatz model**(MK)- Small world property
- Definition of the WS model
- Characters of the WS model
- Navigability in small-world networks (Kleinberg algorithm)

**Scale-free networks, Barabási-Albert model**(MK)- Scale-free property and observations
- Vulnerability and robustness
- The BA model
- Alternative models of scale-free networks

**Motifs and communities**(MK)- Motifs in static networks
- Communities – basics
- Modularity based methods: Girvan Newman algorithm, Louvain algorithm
- Overlapping communities: Link-communities, Clique percolation
- The Infomap method
- Network benchmarks

**Temporal networks**(MK)- Time-scales and representation
- Micro- and macroscopic measures of temporal networks
- Correlations in temporal networks
- Random reference models of temporal networks
- Generative models of temporal networks

**Spatial networks**(MK)- Definition, representation, and characterization
- Simple models of spatial networks
- Human mobility – the gravity law – the radiation law

**Multilayer and multiplex networks**(MK)- Definition and representation
- Characterization and general measures
- Interdependent networks
- Cascading failures in interdependent networks

**From data to networks**(MK)- Network construction from data
- Statistical analysis and fitting methods
- Sampling and biases
- Visualization and applications

###### Books:

- M.E.J. Newman, Networks, an Introduction (Oxford University Press)
- D. Easley, J. Kleinberg, Networks, Crowds, and Markets (Cambridge University Press)

###### Reviews:

- M.E.J. Newman, The structure and function of complex networks, SIAM Review 45, 167-256 (2003).R. Albert, A-L. Barabási, Statistical Mechanics of Complex Networks, Rev. Mod. Phys. 74, 47-97 (2002)