Complex Networks

CR07 Master 2 course organised by
  • ENS Lyon Computer Science Department
  • IXXI – Rhone Alpes Complex System Institute

24 hours lecture + 6 hours tutorial (4 ECTS)



Office: ENS Lyon, IXXI, site Monod, M7.1H24
Tel: +33 426 233 805


Lorenza Pacini –



The course provides an introduction to complex network theory by walking through the established methods and the most recent techniques of modeling and analyzing structured complex systems. During the course we will define the general properties and measures of complex networks, fundamental network models (ER networks, SW networks, BA networks), structural phase-transitions, node and link centrality measures, network modularity and community detection methods, temporal, multiplex and spatial networks, and network construction practical analysis.

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 2018 – January 2019

  1. Introduction and general network characteristics
    • Complex systems as complex networks
    • Representation of complex networks
    • Characteristic measures of complex networks
  2. Advanced network characteristics
    • Advanced measures
    • Centrality measures
    • similarity measures
  3. Percolation and Erdös-Rényi random networks
    • Percolation phenomena
    • Definitions and statistical properties
    • Structural phase transition
  4. Configuration model networks
    • Definitions and statistical properties
    • Stochastic block models
  5. Small-world property, Watt-Strogatz model
    • Small world property
    • Definition of the WS model
    • Characters of the WS model
    • Navigability in small-world networks (Kleinberg algorithm)
  6. Scale-free networks, Barabási-Albert model
    • Scale-free property and observations
    • Vulnerability and robustness
    • The BA model
    • Alternative models of scale-free networks
  7. Spreading processes on networks
    • The SI, SIS, SIR models
    • Conditions of epidemic outbreaks
    • Critical behaviour
  8. Motifs and communities
    • 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
  9. Temporal networks
    • 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
  10. Spatial networks and mobility
    • Definition, representation, and characterization
    • Simple models of spatial networks
    • Human mobility – the gravity law – the radiation law
  11. Multilayer and multiplex networks
    • Definition and representation
    • Characterization and general measures
    • Interdependent networks
    • Cascading failures in interdependent networks
  12. From data to networks (MK)
    • Network construction from data
    • Statistical analysis and fitting methods
    • Sampling and biases
    • Visualization and applications
  • M.E.J. Newman, Networks, an Introduction (Oxford University Press)
  • D. Easley, J. Kleinberg, Networks, Crowds, and Markets (Cambridge University Press)
  • A.L. Barabási, Network Science (Cambridge University Press)