Pardon, I had meant to the tags of this thread. Adding db_errors to your set of tags that you follow will make the db_errors discussions show up in your G2G feed. Adding db_errors to your set of tags that you have defined this G2G thread in will make it more easily seen by people watching the db_errors project.
We have methods for quantifying things like this. I don't think there's exactly the kind of solution you're looking for, but I think it could be made or might already be made, and I think it would be very useful to you and the other members of Wikitree.
We could probably actually define an unconnected tree based off of error codes in connected profiles. We can then graph using a traversal of the family graph. Disconnected graphs will always be closed with respect to the largest main family graph, so we can do comparisons to ask whether one graph is larger than the other, so you can search and sort quickly using a number of algorithms including the bubble sort or the merge sort. Counting the profile nodes of the graph is the basic method for quantifying the size of the isolated graph.