I can't thank you enough for all of your help. As someone mentioned (I believe) I did contact Dr. Strahalm, who helped verify the address.
Since the family was Catholic, I looked up the Catholic churches which were in Graz in 1910 and tried comparing those with the address Dr. Strahalm gave me. The closest I could get was St. Joseph's Catholic church, which is on the East side of the River Mur and Wienerstrasse runs along the west side of the river.
Which prompted me to write the Catholic Diocese in Graz and ask if they had any information on the family they would be willing to share. They wrote back quite quickly that they had no record of a Johan(n) or Anton(e) Joseph Ranner in their church records. The person who contacted me further suggested that had Anton(e) Joseph been born in Graz there would have been birth records for him, and that led him to believe they had moved to Graz from another city.
I have waded through all of the addresses in the online listing of Ranners living in Graz as suggested in this forum (Thank you!!) and compiled a list of people potentially related to me to whom I will send letters. It took me much longer to write the letter in both English and German, not to mention the apology I included for my poor German. =) The envelopes are addressed and the letter printed out in both languages folded and tucked inside... and as I typed this out just now it occurred to me that it might perhaps be wise to include a drawing of the family tree as I understand it to be.
I very much appreciate all of your help, thoughts and comments. I was at a stand still before posting here.