Six degrees of separation, explained. A few random shortcuts turn an orderly network into one where everyone is surprisingly close — while staying locally clustered.
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Watts-Strogatz rewiring
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Start with an orderly ring where everyone knows their neighbors, then randomly rewire a few connections. Even a handful of long-range shortcuts collapses the average path length — the six-degrees-of-separation effect — while keeping high local clustering. This small-world structure appears in social networks, the brain, and power grids.
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How it works
The Watts-Strogatz model starts from a ring lattice and rewires each edge with probability p. Even a small p adds long-range shortcuts that collapse the average path length dramatically, while local clustering stays high. This small-world regime describes social networks, neural wiring, and power grids, and explains why rumors and epidemics spread so fast.
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