If I remove the extra space and just write c(a1), the box fits the size nicely. However, I save and exit and then reload, this extra space reappears cluttering the entire view.
Here is the corresponding GraphML file
Which version of yEd are you using (see "Help" -> "About")?
Which version of Java are you running yEd on (again see "Help" -> "About")?
Can you upload a sample GraphML file that exhibits the problem here? (See How to upload files to yEd Q&A? for details on uploading files here.)
I cannot reproduce this problem.
I downloaded your file, selected the top left edge, clicked the "..." button from the edge's "Text" property, removed all the whitespace, saved the file, re-started yEd, and re-opened the file. No extra whitespace reappeared - the text was exactly as saved. I also tried all other text editing methods yEd offers and it always worked as expected.
Are you sure you are actually saving your edits? And if so, are you sure you are opening the modified file and not the original, unmodified one? Moreover, have you tried saving your edits to a new file instead of overwriting the original file?
This is the result of my edits (I changed the line color of the edited edge to red).