Six degrees of separation is not a figure of speech, it is a geometric consequence of a few shortcuts. Take a ring of near neighbours, add a handful of edges cutting across, and the average distance between any two nodes drops to a few steps: the small-world structure described by Watts and Strogatz. With the same node and edge counts, preferential attachment in the Barabási–Albert style instead breeds a few super-hubs, so once a hub is infected the red wave sweeps the graph far faster than in a random network of even degree.
Six degrees of separation is not a figure of speech, it is a geometric consequence of a few shortcuts. Take a ring of near neighbours, add a handful of edges cutting across, and the average distance between any two nodes drops to a few steps: the small-world structure described by Watts and Strogatz. With the same node and edge counts, preferential attachment in the Barabási–Albert style instead breeds a few super-hubs, so once a hub is infected the red wave sweeps the graph far faster than in a random network of even degree.
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