(Note: capital "I"). The Internet is the largest internet (with a small "i") in the world.
(Note: not capitalised) Any set of networks interconnected with routers.
Now that's just awful. The largest internet is the Internet. All other internets are just internets and not the Internet. Blech, no thanks; I'll take on Wired's editorial policy as my own. (Who has heard anyone refer to a small, local network be referred to as an internet anyway?)
(My own suspicion is that internet wouldn't be capitalized by very many people if Microsoft's Word didn't capitalize it for you without asking.)