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The removal of the average weak tie does more damage than the removal of the average strong tie when it comes to diffusion of information in a social network. Often the shortest and only connection between different nodes in social network are weak ties.
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.
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.