in php friend system, how to print from friend table friends of my friends

in php friend system, how to print from friend table friends of my friends

I have created a friend system in php. A table called friends, has 3
columns. First for friends_id, second user_one and third user_two.
Friends(friends_id, user_one, user_two). Where user_one and user_two are
the ids of the users that are friends.
The following piece of code prints me friends of my friends.
<?php
$friend_query = mysql_query(" SELECT `user_one`, `user_two` FROM
`friends` WHERE `user_one`='$session_user_id' OR
`user_two`='$session_user_id' ");
while($run_friend = mysql_fetch_array($friend_query)){
$user_one = $run_friend['user_one'];
$user_two = $run_friend['user_two'];
if($user_one == $session_user_id){
$user = $user_two;
}else{
$user = $user_one;
}
$friend_id = getuser($user, 'user_id');
$friend_query_two = mysql_query(" SELECT `user_one`, `user_two` FROM
`friends` WHERE (`user_one`='$friend_id' and `user_two` !=
'$session_user_id') OR (`user_one`!='$session_user_id'
and`user_two`='$friend_id' ) ");
while($run_friend_two = mysql_fetch_array($friend_query_two)){
$user_one_two = $run_friend_two['user_one'];
$user_two_two = $run_friend_two['user_two'];
if($user_one_two == $friend_id){
$user_two = $user_two_two;
}else{
$user_two = $user_one_two;
}
$friend_id_two = getuser($user_two, 'user_id');
echo $friend_id_two;
} //end while first
} //end while second
?>
My code works fine, but how can I modify it in order to make it print only
the friends of my friends that happens not to be my friends? (because some
friends of my friends, happens to be my friends as well).