From Mapping the Internet:

The researchers’ results depict the Internet as consisting of a dense core of 80 or so critical nodes surrounded by an outer shell of 5,000 sparsely connected, isolated nodes that are very much dependent upon this core. Separating the core from the outer shell are approximately 15,000 peer-connected and self-sufficient nodes.

Take away the core, and an interesting thing happens: about 30 percent of the nodes from the outer shell become completely cut off. But the remaining 70 percent can continue communicating because the middle region has enough peer-connected nodes to bypass the core.