How to make a circle and a line ending (at the centre of the circle) lock and move together?

I'm new to Illustrator and perhaps it's not the best software of CS6 Master for doing this, but:
I have a few (13) circles, they are connected with lines (one line from the centre of a circle to the centre of the next one, so 13 connecting lines). I need to move the circles around in order to create the appearance that suits me best, but I want the connecting ending to move together (see picture below). I need to do this often and get an immediate visual feedback. How do I do it? Am I using the wrong software altogether?
Thanks in advance to all who will try and help out!

Here's a way of doing it with the Appearance panel and multiple fills converted to an ellipse.
1 You create your path with all the segmentts you require can be an open or closed path.
2. Convert the fill only to an Ellipse. Effect>Convert to Shape>Ellipse (use the Absolute option and give it the dimension you want the circle to be) (cn cahnge this at anytime in the future as well as the color of the circles)
3. Using the Effect>Distort and Transform>Transform move the circle fill to a position corresponding to an anchor of the path as to position the circle with the nchor as the center.
4. In the Appearance panel Option (Alt) drag the fill with the convert to ellipse and the transform down or up to duplicate it, or se the flyout of the Appearance panel to duplicte the fill.
(do this for each circle you need) You will only have to adjust the transformation vertical and horizontal positions, Bith effects will be duplicated when you copy the fill so you only adjust the transformeffecct that is already associated with the fill.
Like this:

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How to make a circle and a line ending (at the centre of the circle) lock and move together?

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