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I have a web of boxes 'connected' (via beziers drawn on top of them) and I want to be able to select a box + the ends of the bezier on that box, to move the box + its connections around.

I have 20+ boxes, and over 100 lines, so the only way I can seem to do it now is to click every end point individually so hopefully there is a better way!

Is that possible?

Edit 1: The lines must not all go to the same point, the position they are attached to in the box is important

Edit 2: Might be important to say, these are initially generated via Python (SVG files) so i'm not sure if it's easy to convert them to diagram connectors

Here is a small example somewhat showcasing what I'm working with: enter image description here

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Convert the rectangle to paths by selecting it and clicking Path > Object to Path, or Shift+Ctrl+C

Select everything with the Select and Transform Objects Tool F1

Switch to the Edit Paths by Nodes tool F2, then hold down Shift while clicking and dragging to select all the nodes of the rectangle plus the bottom nodes of the curves. Select any additional nodes in the same way.

Grab one of the highlighted nodes, and move it, and all the selected nodes will move together.

Example

enter image description here

Note: these curves you show in your example are BSplines, technically they're not Bézier curves, but these work just fine in Inkscape too. You can also use the Bézier tool (aka the Pen tool), and create BSplines by selecting that option in the Tool Controls along the top.

enter image description here

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