CS-E5745 - Mathematical Methods for Network Science D, Lecture, 11.1.2024-15.2.2024

Översikt

• 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). You need lecture notes (slides), patience, and focus to solve the problem sets. You, of course, need prior knowledge of calculus and linear algebra. For a quick review of linear algebra, if required, you can watch the 3Blue1Brown series, and for more details, you can see Introduction to Linear Algebra by Gilbert Strang or The Oxford Linear Algebra for Scientists.
  

  
  If you have not completed the Complex Networks course (CS-E5740 - Complex Networks), you can have a look at these materials to get the motivation for why we are doing this course:
  

  • The Emergence of Network Science
  • Twenty years of network science
  • Bridging the gap between graphs and networks
  • Complexity Explorables (A collection of interactive explorable explanations of complex systems in biology, physics, mathematics, social sciences, epidemiology, ecology and other fields...)

  
  

  If you are interested in alternative materials, 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
  • The Nature of Complex Networks by Sergey N. Dorogovtsev and José F. F. Mendes
    
  • 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!

  • Välj aktivitet Introduction

    

    Introduction Fil PDF
  • Välj aktivitet Lecture 1

    

    Lecture 1 Fil 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
    • Ref: Newman 2018, Ch 11 - 12

    
    

  • Välj aktivitet Lecture 2

    

    Lecture 2 Fil 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

    
    

  • Välj aktivitet Lecture 3

    

    Lecture 3 Fil 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

    
    

  • Välj aktivitet Lecture 4

    

    Lecture 4 Fil 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

    
    

  • Välj aktivitet Lecture 5

    

    Lecture 5 Fil 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

    
    

  • Välj aktivitet Lecture 6: Project

    

    Lecture 6: Project Fil PDF

    • Older Slides
    • Ref: Message passing methods on complex networks by M. E. J. Newman
    • See Project. Video from 2022-02-17

    
    

  • Välj aktivitet Probability generating functions cheat sheet

    

    Probability generating functions cheat sheet Fil PDF

    In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. See https://en.wikipedia.org/wiki/Probability-generating_function.