Closing Remarks

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In this tutorial, we began with the Small World Phenomenon: The idea that short paths exist between random agents, even though a graph is highly clustered. This phenomenon may seem counterintuitive at first. However, such small world networks have been shown to exist in some seemingly unlikely places, such as the U.S. power grid.

We hope to have shown that small world networks are in fact quite natural, and a result of the introduction of a small amount of randomness into a graph's local structure. The remarkable properties of these networks show the substantial effect that small changes at the local level can have on the global properties of a graph.

These properties can be both static and dynamic. A small world graph can have its own characteristic behavior in a dynamical system. To approximate a small world graph by a highly structured or random graph can create vastly different results, whether the simulation concerns disease spread or social norms. In studying such phenomena, we need to recognize the impact that a small world structure can have.

If you wish to further investigate such small world societies you can access the Small World connection algorithm through the main simulator. Many other connection algorithms are also provided, including the Solaris algorithm. You may want to experiment and see the effects of connecting various societies using different methods and parameters and explore what effect this has on path length and clustering, as well as on many other potential measures and graph properties.

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