Topic outline

  • General

    In this course we will go through some of the more mathematical topics in network science. The aim is to develop skills in doing pen-and-paper calculations and understanding the analytical methods that are most common in network science. 


    Topics

    - Percolation: generating functions, excess degree distributions, component size distributions, Galton-Watson process

    - Processes on networks: spreading models, network evolution models, rate equations, binary state dynamics

    - Random graphs, graph ensembles, exponential random graphs

    - Stochastic block models

    - Multiplex and multilayer networks: mutual percolation (possible topics for project work)


    Prerequirements

    The students are expected to have completed the Complex Networks course (CS-E5740 - Complex Networks) and basic mathematics courses at Aalto, or have at least equivalent background knowledge. Courses on stochastic processes or discrete mathematics can be useful but we do not expect the students to have taken any.

    Workload

    The course does not have an exam, but passing and grading is based on returning 5 sets of homework assignments and the "final project" and participating in 5 homework sessions (Wednesdays 12.15 - 14.00). There is also 6 lectures and a voluntary contact class every week where students can ask for advice on solving the problems. To get grade 1 the students are expected to successfully complete at least half of the exercises.

    Grading

    A grade between 0-5 is given to the students based on the returned homework problems and the project. In order for the homework problems to be graded the students must participate in the homework sessions and mark each problem they want to return as done. If the problem is marked as done the student is expected to be able to present it on the whiteboard.