The internet architecture has been decentralized for safety since before most of us knew there was such a thing: back in ARPAnet days, the department of defense wanted a network that could survive a nuclear attack.

There might be some vulnerability in some kinds of relatively low-level hardware: e.g., if your characters could find a way to destroy all the routers from a particular large company, that might bring the Internet down temporarily. "Temporarily" because people would be working hard to patch in other devices that didn't have the vulnerability in question, and get their sites connected again at least partially.