Tutorial: Small World

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The Small World Tutorial

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

This tutorial is an exploration of what is known as the Small World Problem. It is adapted from the paper, "Networks, Dynamics and The Small World Phenomenon," by Duncan Watts. This tutorial is intended to serve as an aid to this paper and attempts to demonstrate Watts's method and results. Readers wishing to gain further information on this topic should consult the above paper.

TABLE OF CONTENTS

1. Introduction
1. The Small World Phenomenon
2. Isolating the Small World Problem
2. Describing a Small World Graph
1. Formal Measures
2. Caveman Graph
3. Random Graph
3. Creating a Small World Graph
1. A Refined Definition of Small World
2. A Recipe for a Small World Graph
3. Graphs with Intermediate Alphas
4. Replotting the Data
5. Generalizing the Procedure
4. Dynamic Properties of Small World Graphs
1. How does a Small World Behave?
2. A Simple Model of Disease Spread
3. Implications for Social Modeling
5. Small World Graphs Revisited
1. Finding Short Paths Between Agents
6. Closing Remarks

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