Deforming triangulation

Hello

Wondering if there is any way to group/move nodes on multiple objects.

I am deforming triangulations.  Triangulations consist of over 100 points [small circles] and, for internal points, from each point 6 edges [2 point straight lines] each going to a different point.

I want to move a circle and the nodes of its 6 lines.  I can do each point and the six line nodes in seven actions, is there any way I can group to do in a single action?

Thanks for your time.

Glenn