Contagion models on multilayer and higher-order networks

Summary

In this lecture, we will discuss the basic concepts of multilayer and higher-order networks. We will focus on spreading processes on top of these structures. The idea is to use the motivation of contagion processes to construct a stochastic process on top of graphs, multilayer, and higher-order networks. In the first half of the lecture, we will construct such a process using simple and fundamental building blocks (i.e., a structure, a set of local rules, Bernoulli random variables, and Poisson processes). In the second half, we will extend these ideas to more complex models (i.e., multilayers and higher-order networks). This part will focus more on new results and open problems in this area. The main goal of this course is to provide students with the tools to propose, model, and study new processes.

Date and duration

Date:

29/05/2021

Duration:

3h

Material

Slides

Slides (pdf)

GitLab – code for disease spreading in multilayers

GitLab – code for social contagion on hypergraphs

Contagion models on multilayer and higher-order networks

1. Network structures

   1.1 Single-layer networks (graphs)

   1.2 Multilayers

   1.3 Hypergraphs

2. Brief probability and stochastic processes recap

   2.1 Bernoulli Random variables

   2.2 Bernoulli and Poisson processes

3. Spreading processes in networks

   3.1 Constructing spreading processes in networks

   3.2 Monte Carlo simulations

   3.3 (Extra) From exact to mean-field approximations

   3.4 (Advanced) Temporal Limitations

4. New behaviors in multilayer networks

   4.1 Disease localization and spectral properties

   4.2 (Extra) Spectral properties and quotient graphs

5. Contagion processes in higher-order networks

   5.1 The social contagion model

   5.2 (Extra) Multistability and Intermittency

   5.3 (Advanced) Hybrid Phase transitions

   5.4 A “general” framework

   5.5 Future perspectives

Main references

1. Fundamentals of spreading processes in single and multilayer complex networks: Original , arXiv

2. Contagion dynamics on higher-order networks: arXiv

For more references, see the slides. Each section has a slide with specific references.