CS-E5745 - Mathematical Methods for Network Science D, Lecture, 13.1.2022-17.2.2022

Topic outline

• Material & Resources
  The main idea behind this course is learning by doing. Lectures are mainly based on Networks by M.E.J. Newman (2010 or 2018). To solve the problem sets, you just need the lecture notes (slides) and a bit of patience and focus. You of course need prior knowledge of calculus and linear algebra. For a quick review on linear algebra, if needed, you can watch 3Blue1Brown series and for more details, you can see Introduction to Linear Algebra by Gilbert Strang.
  

  
  

  If you are interested, you can also have a look at the following resources to follow this course or go in more depth for some of the topics:

  • Network Science, Barabási/Pósfai, ONLINE FREE EDITION
    
  • Complex Networks: Structure, Robustness and Function, Reuven Cohen and Shlomo Havlin
  • A First Course in Network Science by Clayton A. Davis, Filippo Menczer, and Santo Fortunato

  
  

  For more mathematical approaches:

  • Random Graphs and Complex Networks, R. van der Hofstad (2016-2017)
    
  • A First Course in Network Theory, Ernesto Estrada and Philip A. Knight
  • Probability on Trees and Networks by Lyons and Peres
    
  • Computer Age Statistical Inference: Algorithms, Evidence, and Data Science by Bradley Efron and Trevor Hastie

  
  You can watch this video by Mark Newman to see how the 2021 Noble Prize in Physics is related to the problem of community detection in networks!
  

  • Select activity Introduction

    

    Introduction File PDF
  • Select activity Probability generating functions cheat sheet

    

    Probability generating functions cheat sheet File PDF
  • Select activity Lecture 1

    

    Lecture 1 File PDF

    1. Basic concepts and notation (remind CS-E5740)
    2. Basic network models (remind CS-E5740)
    3. Random graphs and common approximations:
       Tree-like approximations
       Thermodynamic limit
       

    • Lecture video
    • Last year recorded video
    • Ref: Newman 2018, Ch 11 - 12
      
  • Select activity Lecture 2

    

    Lecture 2 File PDF

    1. Generating functions and their use in networks
    2. Percolation Theory and Critical Phenomena
       
    3. Branching processes (Galton-Watson process for networks)
       

    • Last year recorded video
    • Ref: Newman 2018, Ch 12, 15 - Newman 2010, Ch 13
      
  • Select activity Lecture 3

    

    Lecture 3 File PDF

    1. Generating functions and their use in networks
    2. Percolation Problems and Components of a Graph
       
    3. Branching processes (Galton-Watson process for networks)
       

    • Last year recorded video
    • Ref: Newman 2018, Ch 12, 15 - Newman 2010, Ch 13
      
  • Select activity Lecture 4

    

    Lecture 4 File PDF

    1. Dynamical models of/on networks
    2. Spreading models on networks

    • Last year recorded video
    • Ref: Newman 2018, Ch 12, 13, 16 - Newman 2010, Ch 14, 16
      
  • Select activity Lecture 5

    

    Lecture 5 File PDF

    1. Exponential random graphs (ERGMs)
    2. Stochastic block models (SBMs)

    • Last year recorded video
    • Ref:
      Newman 2018, Ch 14.1, 14.4 - Newman 2010, Ch 15.2
      Aaron Clauset's lecture note
      
  • Select activity Lecture 6: New Topics & Project

    

    Lecture 6: New Topics & Project File PDF

    See Project.
    

    
    

    • Video from 2022-02-17
    • Last year recorded video