A social network can be characterized as a system of mutual relationships between people of some groups. Such networks are often expressed as graphs. Formal concept let us have the ability to find good enough relations for a group based on common properties. But the "quality" of the relations from Formal concept cannot be measured. That means we just know the existence of a relation, but we don't know how good or close of the relation. There must be a method to evaluate the "quality" of these relations. A relation is good or not might be decided by the person who cares about it. For different users, a same relation may be good or not good. So the evaluation of the "quality" of a relation would be given based on users' expectation. CTL is used in this paper to define the properties users caring about. An augmented formal concept is given in this paper to support the relation discovery on weighted SNS network. A user oriented relation quality measurement method is put forward based on CTL and AFC. Using this method, a quality evaluation could be made from the user's point of view.