Before you get excited at seeing any names on any of the graphs here, please be aware that they're all randomly generated and bear no resemblence to the names, or even gender, of the real matches.
Having got the data to do what I wanted, and displayed it on the screen, the next step is to work out what it actually means. Fortunately people grouped up into structures rather than just being a few pairs linked together, which in theory should help to start identifying which trees people share common ancestors with.
This looks pretty simple to me - each of the people in this group are linked to all the other people. Its a pretty strong indication that they are related in the same way. Huzzah. A bit of a sanity check says that yes, they all overlap on chr-3 in the same spot.
At a first glance, I thought this was a simple thing where the 6 people in the lefthand side structure (Ann Beard, Brian Cortez, Andrew Barber, Alan Arellano, Adam Anthony and Bruce Delgado) were all related through one shared ancestor, and then 4 people in the righthand structure (Alan Arellano, Adam Anthony, Bruce Delgado and Carlos Escobar) were all related through another shared ancestor. So effectively Adam Anthony, Bruce Delgado and Alan Arellano would be closer to me (larger nodes, longer shared cM chunks, etc) that the Escobar and the others on the left.
However, this is the chromosome browser with Ann Beard in
orange, Barber in blue, Delgado in green, Escobar in pink and
Arellano in yellow.

As you can see, they actually all match on the same spot on
chromosome 2, its just that the fragments that persist between
me and Escobar are smaller, and don't constitute a match for
Beard and Barber. Oddly I also match a >5cM chunk for Escobar
on another chromosome.
This highlights that while the graphs might be useful to show potential relationships, they don't convey all the information, and its definitely worth following up with other tools you have available.
Incidentally, Arellano and Anthony are my 2nd and 3rd closest matches, at 2-4th and 3-5th cousin range.
This, on the other hand, does probably show two seperate branches, as well as a scattering of small single matches that are harder to categorise without more matches.
The largest node, despite the randomly assigned male pseudonym, is my aunt (genetically half-aunt, for what its worth), and she appears to be related to two seperate branches: April Black, Anthony Becker and Brian Duffy; and Brent Chase, Brenda Castaneda, Angela Barrera and Carl Duran.
Black, Becker and Duffy all cluster at the end of chr4, and matching at 3rd-5th for two of them, and 4th-distant for the other. Chase, Castaneda, Barrera and Duran all cluster at the end of chr16 and Chase matches at 3rd-5th and the others at 4th-distant.
So they are two seperate groups, both related down the same side as my aunt. So far, that seems to back up that this is producing potentially useful clumps. If only my matches weren't so remote.