How can I write FQL query for getting information on How a specific user is connected to logged in user (X degree of connection) similar to linked in as shown in the image
From image the tooltip (Nuno.B is a 3rd degree connection)
Given an user ID how to find the nth degree of connection in faceBook api 2.0. Will it be possible to get this ?
No, this is not possible. You can only determine whether two user_id are friends or not, see https://developers.facebook.com/docs/graph-api/common-scenarios#userfriends