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Here's an illustration from their original paper : is small, the randomness will not strongly affect the clustering of the regular model.I like to use a "coarse graining" approach to understand why the small-world effect occurs in the Watts-Strogatz model.This means that closed loops of length 3 are quite likely.In the language of network theory, social networks tend to have a high , and this calls into question our neglect of closed loops.Thus, the "six" can be thought of as a gesture in the right direction.At a basic level, the mechanism that's responsible for keeping distances short, even in networks with a lot of nodes, is the following: if you pick a node, start traveling outward from it, and count how many nodes you can reach within . Thus, in a few hops, you can reach a huge number of nodes.
For a more complete argument, I recommend this Coursera course .
In highly regular networks where every node is just connected to its immediate neighbors, the typical path length can scale linearly in network size and, thus, not exhibit the small-world effect.
Social networks tend to have close to, but not exactly, this structure.
He instructed them to try to get the packages to a specific person in Boston.
However, they were asked to only directly send the package to someone whom they knew on a first-name basis.
Suppose we take the middle network in the figure approach and "coarse grain" it into blocks of Roughly speaking, if we think of each block as a node, it forms a random network with the other blocks.