Construction of Small-world Networks
The main mechanism to construct small-world networks is the Watts-Strogatz mechanism.
Small-world networks can also be introduced with time-delay, which will not only produces fractals but also chaos under the right conditions, or transition to chaos in dynamics networks.
Degree-Diameter graphs are constructed such that the number of neighbors each vertex in the network has is bounded, while the distance from any given vertex in the network to any other vertex (the diameter of the network) is minimized. Constructing such small-world networks is done as part of the effort to find graphs of order close to the Moore bound.
Another way to construct a small world network from scratch is given in Barmpoutis et al., where a network with very small average distance and very large average clustering is constructed. A fast algorithm of constant complexity is given, along with measurements of the robustness of the resulting graphs. Depending on the application of each network, one can start with one such "ultra small-world" network, and then rewire some edges, or use several small such networks as subgraphs to a larger graph.
See also: Diffusion-limited aggregation, pattern formation
Read more about this topic: Small-world Network
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