NetworkSimulations

By Matthew Osborne

This repository stores all of the code I have written in order to examine the behavior of incidence curves of complex contagion over various network topologies.

What is a Complex Contagion?

A complex contagion is a contagious process (like a disease or behavior) in which a certain ammount of reinforcement or cooperation is needed in order for the contagion to spread. In our particular code we are considering a model presented by Watts in "A simple model of global cascades on random networks" in which you consider a contagion spreading on a network. In order for the contagion to spread from a contagious node to a susceptible node the susceptible node must have a fraction of contagious neighbors that is larger than a certain threshold. For example, I have five friends and a threshold of 1/2. If 2 of my friends are contagious but 3 are not it will not spread to me. However if 3 or more of my friends are contagious it will spread to me.

How I model the spread

For a given network, I initially infect a certain fraction of the nodes. Then the disease spreads over the network using a Gilespie algorithm. This is all facilitated with python's networkx package.

In this repository

The repository is split into two folders, one that contains all of the code I have used to run the simulations. The other contains code that cleans the data and creates pictures of the incidence vs the number of currently infected nodes in the network.

SimulationCode Folder

There are three file types.

1. Simulation.py - this file contains all of the code for running the simulations.
2. CreateNetworks.py - this file contains all of the code for creating the various networks I simulate on.
3. Simple/Complex*.py - these files are scripts for running complex or simple (threshold = 0) simulations on a * random graph.

PicCode Folder

This folder contains two types of files.

1. Aggregate*.py - these files will take the saved file from the simulations on a * random graph and aggregate the data for plotting purposes.
2. Make*Pics.py - these files will take the aggregated data and create a plot of number of infecteds vs incidence for the * random graph simulations.

DataCode Folder

This folder contains code I used to clean some data from various real life social networks. In particular the networks found here.