Could one be a friend of all? The social network "ILM" has a lot of members. It is well known: If you choose any 4 members of the network, then one of these 4 members is a friend of the other 3. 

Proof: Is then among any 4 members always one who is a friend of all
  members of the social network "ILM"?

Note: If member A is a friend of member B then member B is also a friend of member A.
I don't find an approach right now. Any kind of help or advice will be really appreciated.

Suppose there isn't a person who knows everyone.
Then take vertex $v$, he doesn't know everyone, in particular there is a $w$ he does not know.
If $w$ doesn't know anybody we are done, if he does select a friend of $w$, Preferably somebody who does not know somebody besides $v$ (if everybody that knows $w$ knows everybody except possibly $v$ you can argue that everybody who knows $w$ does not know $v$, hence you can pick any other two vertices and there will be no one knowing all three). So suppose there is a friend of $w$ called $u$ that does not know someone else called $t$. In the group $v,w,u,t$ there is no one who knows the rest.
