Before revision:  When the support of the first marginal is a finite set, we give a necessary and sufficient condition for the WEP to hold in terms of the new concept of 2-net  . Finally, we study the relation between cycles and extremality.
After revision:  When the support of the first marginal is a finite set, we give a necessary and sufficient condition for the WEP to hold in terms of the new concept of 2-net and deadlock . Finally, we study the relation between cycles and extremality.