To further illustrate this point, LinkedIn provides a helpful directory at the bottom of their homepage, allowing one to browse every user[0] and every company[1] in their graph. Hard pressed to argue that it's illegal to navigate to every single profile if you serve a directory of them.
Also, I believe there are companies[2] and shops[3] that specialize in doing that kind of thing. I would say it would be worth reaching out to them, if nothing else just to get a sense for what something like that would cost.
0 = https://www.linkedin.com/directory/people-1-5-1/ 1 = https://www.linkedin.com/directory/companies 2 = http://scrapinghub.com/ (makers of the outstanding Scrapy framework!) 3 = http://webscrapinghelp.com
Selling it is a different matter, and one that I don't have enough law background to answer. It may fall under the provision in US copyright law that says that facts are not copyrightable. So long as you are just selling the facts of the graph that they gladly serve to the Internet, ... again, I am not experienced enough to comment.
I believe there are web scraping companies that sell monthly dumps of LinkedIn data, but I don't know off-hand how much something like that would cost.
It would also likely depend on whether you wanted US-only data or worldwide.