Prove that in a graph a group of even nodes there are two of degree at least $2$ We have just started learning graphs, and I understand the concept clearly, but when it comes to proving something I just don't know how to start!

Prove that in in a group of an even number of people there are at least two of them that the number of the common people that they know is even.

So I translated it to a Graphs problem:

Given a graph $G$ (not directed; knowing someone is mutual), prove that in every group of an even number of vertices there are at least two vertices that the number of their common neighbors is even

I understand that this is not of the hard questions, but I just can not think the methods of proving such things in Graphs in my head, yet. I would be happy for a direction!

You can find a nice solution here.
