Same Number of Handshakes

At a dinner party, many of the guests exchange greetings by shaking hands with each other while they wait for the host to finish cooking.

After all this handshaking, the host, who didn't take part in or see any of the handshaking, gets everybody's attention and says: "I know for a fact that at least two people at this party shook the same number of other people's hands."

How could the host know this? Note that nobody shakes his or her own hand.