How can I set an arrowhead "back" from the end of a line?

Question

I am drawing a graph (network), like this:

I would like to be able to reposition my vertices (grey circles) without having to meticulously reposition all my edges.

Here's what I've tried:

1. draw the edge lines to end at the CENTER of the vertex; then dragging the vertex DOES make all edges still line up correctly, but the arrowheads are inside the vertex (maybe I can set the arrowheads "back" from the end, like how "align" lets me set the arrowheads "forward" from the end?)
2. draw the edge lines to end on the edge of the vertex; then the arrow heads are (correctly) on the perimeter of the vertex, but moving the vertex results in incorrect edge placement:

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Is there a way to do this that doesn't require a ton of meticulous work?

Answer 1

If it must happen in Illustrator, not in any external flowchart application, you can do this:

In the left all black items which will be moved are selected with the direct selection tool by dragging from corner to corner over the area marked with the red dashed rectangle.

In the right the selected items (=all selected anchor points) are moved with the direct selection tool.

This unfortunately causes the arrows do not any more point to the center. As a workaround you can use a custom arrowhead which has the visible part at a carefully selected distance from the line end. You can use only circles which have a certain diameter and white fill. The line starts and ends at the center of the circle as you have already tried.

Making custom arrowheads is shown in numerous tutorials.