Pigeon Hole principle

Consider a party of n people (where n is even and n > 11). Clearly, everyone knows themselves. If n/2 of the peolpe know exactly 1 person other then themselves and n/2 of the people know exactly 5 people other than themselves:

1) Prove there is at least 1 person known to 4 people

2) Suppose that one of the people knows exactly 1 person realized that they knew someone else, which means that they know exactly 2 people other then tehmselves. Does this make a difference? Can there now be at least 1 person that is known to 5 people or does this not make a difference at all. Explain your answer.

I know this problem can be done by pigeon hole principle (probably the easiest way to do it) but I don't see what are the "boxes" are and I think that the n people are the pigeons. Anyone got any ideas?

use graph theory and with two vertices (people) joined by an edge if they know each other. then show that there exists at least one vertice v of degree 4.

can't be bothered to rephrase the second in therms of graph theory.