Given two people and a set of all persons with ties to either of them, the stronger the tie between the two people the more overlap exists between their friendship circles. Put another way, overlap between two networks is least when there is no tie between those two people.
See also:
 This hypothesis (dyadic ties) comes from The Strength of Weak Ties
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When it comes to network diffusion of information or influence, all bridges (a line in a network graph that represents the only connection between two points) are weak ties.