No one really "runs" the internet. But if you want to know who manages the standards and IP schemes that are used on the internet, it would be IANA (responsible for developing IP schemes), ARIN, RIPE NCC, APNIC, LACNIC, and AfriNIC.
Basically it's just regional companies that work with IANA (the big one) to manage IP schemes globally and make sure things stay standardized. But none of them "run" the internet. They just provide a means of connecting and communicating across it.
I have alphabet soup.
2 minutes ago
Now go to the first blog in the list, THE BIG ONE? -
(Note that's what my unsuspecting friend put in brackets)
To see the real reason why I was sent the right answer - I ANA.