Does the galaxy look like a Web or a Tree?
The process where you link random points within distance $r_0$ into a graph is known as continuum percolation. As $r_0$ increases from 0 at first there are just isolated clusters (binaries, randomly very close stars) that gradually merge. At a critical distance of a few parsecs these clusters mostly merge into one major galaxy-spanning cluster, and above that distance this cluster just gets more densely connected. The big network at the critical range has a scale-free structure of local clusters, bridges, and trees: neither a proper web nor a tree.
Some illustrations from my book manuscript:


It should be noted that these pictures assume a constant star density. In reality the stellar density varies, so for a given $r_0$ there is a part of the disk and bulge that are connected and parts of the outer galaxy and halo that are not connected.