Your original diagram is stored as GraphML, right?
When you open your original diagram and select all group nodes, does this trigger the resizing already?
If not, does the resizing still happen if you turn off "Consider Label" in the "Open Group" property section and after that export to SVG?
One possible cause for the strange resizing could be inconsistent label sizes. The "Consider Label" option forces group nodes to grow in width to be wide enough to contain their label and their state icon. For this to work, yEd has to calculate the size of the group node labels. If the size calculation now returns larger values than at the time you created the diagram, your labels will "grow" and consequently your nodes will grow.
Label size calculation depends on operating system text measuring as well as Java text measuring. Thus any change to your machine or to yEd that affects text measuring might result in the undesired resize effect you are experiencing. E.g. if you work on different operating systems, text measuring will differ. A system update that affects fonts might change text measuring. Changing the Java version on which yEd runs might change text measuring.
Unfortunately, there is one thing that does not fit the "text measuring changed" theory: if text measuring did indeed change and your labels do grow in response to the changed measuring, the undesired growth should happen right when your diagram is first displayed.
I cannot think of a reason why this would happen only after SVG export.
You could try to verify the "text measuring changed" theory using the following approach:
- Start yEd.
- Open an empty document.
- In a second tab, open your original diagram.
- In the original diagram, find a group node that is connected to one of the skewed edges.
- In the empty document, create an empty group node with the same style and style configuration as the group node from step 4.
- Edit the label of the new group node and set to the same text as the the group node from step 4.
- Save the new document as a GraphML file.
- Open the GraphML file of your original diagram and the GraphML file of the new diagram in a text editor.
- In both files, find the <y:NodeLabel ...>...</y:NodeLabel> element that encloses the text from step 6.
- Compare the values of the width attributes of the elements from step 7.