@reiver

Weak Ties Serve To Link Together Different Tightly-Knit Communities: An Example

[W]eak ties serve to link together different tightly-knit communities that each contain a large number of stronger ties. Here, Onnela et al. provided an indirect analysis to address this question, as follows. They first deleted edges from the network one at a time, starting with the strongest ties and working downward in order of tie strength. The giant component shrank steadily as they did this, its size going down gradually due to the elimination of connections among the nodes. They then tried the same thing, but starting from the weakest ties and working upward in order of tie strength. In this case, they found that the giant component shrank more rapidly, and moreover that its remnants broke apart abruptly once a critical number of weak ties had been removed. This is consistent with a picture in which the weak ties provide the more crucial connective structure for holding together disparate communities, and for keeping the global structure of the giant component intact.

[...]

J.-P. Onnela, J. Saramaki, J. Hyvonen, G. Szabo, D. Lazer, K. Kaski, J. Kertesz, and A.-L. Barabasi. Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. USA, 104:7332–7336, 2007.

-- David Easley , Jon Kleinberg

from "Networks, Crowds, and Markets: Reasoning About a Highly Connected World"

Quoted on Thu Feb 21st, 2013