Dynamic Properties of Small World Graphs
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Implications for Societal Modeling
In the disease spread model, the small world graph displays a very short survival time. It acts rather more like a random graph than a structured graph. What is remarkable is that it may be difficult to tell the small world graph apart from the fully structured graph, as only a very small number of random connections are needed to make a graph small world. The implication for disease control is that a disease may actually be far closer than it appears to be. Models that do not take the small world structure into account can yield gravely mistaken results.
In his paper, Watts presents a more sophisticated model of disease spread and demonstrates that the small world structure not only affects the speed of disease spread but also the chance that a disease will infect an entire population.
In another example, Watts conducts a prisoners' dilemma competition on a set of agents in a small world graph. He demonstrates that the small world structure allows cooperation to evolve and spread in a society. These examples shows that a small world graph has its own characteristic set of properties that affect its behavior in a variety of dynamical systems. The small world structure must be taken into account in order to accurately model such systems.
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