Undirected graph conversion to tree

Question

Given an undirected graph in which each node has a Cartesian coordinate in space that has the general shape of a tree, is there an algorithm to convert the graph into a tree, an

Answer 1

A simple solution would be to define a 2d rectangle around the red node or the center of your node and compute each node with a moore curve. A moore curve is a space-filling curve, more over a special version of a hilbert curve where the start and end vertex is the same and the coordinate is in the middle of the 2d rectangle. In generell your problem looks like a discrete addressing space problem.