If we are going to look at profitable online communities then look at MMORPGs. It may be outside the realm of facebook and linkedin but there is plenty of profitability to be had beyond myspace clones or even websites.

World of Warcraft takes in 12.99 - 14.99 per user per month and has approximately 10 million active subscribers. Plus additional profits whenever an expansion comes out.

http://www.mmogchart.com/Chart1.html

faq...

http://www.mmogchart.com/faq/

[EDIT: added "per month" to second paragraph, first sentence]