Exclude edges from participating in the layout

Consider a graph like the one shown below:

Graph taken from the VisJS example site

I would like to be able to display/hide the red edges (forget that they are hand drawn) shown below when the user clicks a button or similar:

Same example with added red edges

I don’t want the red edges to participate in the layout but instead for them to be shown as a kind of overlay. It would be nice if the edges could try to avoid overlapping any nodes in their path, but its definitely not required.

I think if I could set a boolean flag on the edges telling the layout engine to either include or exclude them from the layout setup, it could work. There is a physics parameter on the edge that I can override, but it doesn’t seem to help – the edge still participates in the layout.

I could probably also write some scripting which tracks the nodes and draw the red edges in another graph above, but that is specifically what I want to avoid.