In Edge of Night various nobles are hoping to become the ruler of Ubersreik.
It's last ruler was Graf von Jungfreud. A new ruler would not be the same power as him, would they have same title or a different one? If you rule a city only you are a....?
Cast a spell called "Le Goog" and find THIS. 
The leader of a free city is a Bürgermeister in the history of Germany. Free Citie in the Hanse did not have nobility.
Burgomeister seems to be a title used by whomever is responsible for the city adminstration, if not a noble. Adler is the Burgomeister of Stromdorf under the Von Jungfreud rule.
Graf is the title of the Patriarch of a noble family who have rule of some land, if I'm not mistaken. From the link doc ct gave us, it is the German equivalent of a Count, but I think I saw Counts on Warhammer world that are not Grafs, so I would use it like I'm saying here.
Pedro Lunaris said:
Burgomeister seems to be a title used by whomever is responsible for the city adminstration, if not a noble. Adler is the Burgomeister of Stromdorf under the Von Jungfreud rule.
Graf is the title of the Patriarch of a noble family who have rule of some land, if I'm not mistaken. From the link doc ct gave us, it is the German equivalent of a Count, but I think I saw Counts on Warhammer world that are not Grafs, so I would use it like I'm saying here.
The reason why you can read both "count" and "graf" in warhammer books is because different writers use different words for the same thing. Graf is the German word for count, so whenever you encounter those words, they mean exactly the same thing, During a roleplaying session you could use whichever word you are most comfortable with using.
The "title" of the nobles in Edge of Night will not change, their families will become the liege lords of the town which is currently a friedstadt.