Your post reminded me of some of the work by Mark Granovetter on the strength of weak ties.
Akshay Java

Thanks for the comment. I’m familiar with Granovetter’s work — I even met him once at a Stanford conference on computational social science. And there has been some follow up on Granovetter’s work, e.g. “Tie Strength in Question & Answer on Social Network Sites” by MIT researchers Katrina Panovich, Rob Miller, and David Karger. I also believe there’s been a bunch of work at Facebook and LinkedIn questioning aspects of Granovetter’s theory of the “strength of weak ties” for information transmission.

But I haven’t seen any work tackling the specific research area in my post — namely, the ROI for establishing a professional network.

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