Dynamic Properties of Small World Graphs

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A Simple Model of Disease Spread

Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.

In this model, we begin with a population of N agents, and infect a single agent with a certain disease. In the societies below, healthy agents will be represented by blue circles, and infected agents by red circles. In every time period, each infected agent has a 50 percent chance of infecting each other agent to whom he is connected. We are interested in how quickly the disease will spread. On the left, we have created a highly structured graph. On the right, we have created a small world graph by introducing random connections. Press "Go" to begin the time simulation, and then compare the rates of infection for the two societies.

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