Small-world network
Graph where most nodes are reachable in a small number of steps
Small-world network
A small-world network is a graph characterized by a high clustering coefficient and low distances. In an example of a social network, high clustering implies the high probability that two friends of one person are friends themselves. The low distances, on the other hand, mean that there is a short chain of social connections between any two people (this effect is known as six degrees of separation). Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network, that is: L ∝ log N {\displaystyle L\propto \log N} while the global clustering coefficient is not small. In the context of a social network, this results in the small world phenomenon of strangers being linked by a short chain of acquaintances. Many empirical graphs show the small...
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