Dynamic Properties of Small World Graphs

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How does a Small World Behave?

So far, our exploration into small world societies has only considered their static properties. While this is interesting in itself, it ignores the larger issue of the dynamic properties of such a network. That is, how does such a graph behave? This is a highly relevant question for the social sciences, since the human population appears to form a small world network.

Much of today's literature on Dynamic Systems makes certain assumptions about the structure of populations. For instance, the population is often assumed to be fully connected. Even when this is not the case, the connections are generally assumed to be either fully structured, or completely random. However, a small world graph has both properties of highly structured graphs and of highly random graphs. Thus, the dynamic behavior of a small world graph will likely be very different from either a random or a well structured graph. Introducing these graphs as approximations may severely alter experimental results.

We will present an example of a very simple dynamic system on the next slide and show how the small world structure affects its behavior.

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