What is the best number of habitats in a cluster

Greetings to the list,

I have been having a couple of discussions with list members dealing with
clusters of habitats, this has gotten me to thinking and has raised a few
questions, so perhaps the collective intellect of the list can come up with
some answers.
A couple of definitions first, I refer to a single line of habitats arranged
in a framework as a 1D structure, to get from the habitat at one end of the
line to the one at the other end of the line you have to go through all the
ones in between (I am assuming a framework holding the habitats and an
internal transport system along the framework). A 2D structure would be like
a chess board, a framework in a grid with habitats locked in the frame. A 3D
structure would be like a cube or some other solid shape with the habitats
located at the junction of the grid, a 10 X 10 X 10 grid would hold 1000
habitats.

A single habitat is simple, it is just there by itself, 2 habitats would be
a 1D line, with 3 you could make a 2D structure, 4 makes a good simple 2D
grid, 6 gives you a reasonable simple 3D grid, picture a cube with the
end-cap of each habitat in the centre of each face of the cube. It is pretty
easy to say that this makes a reasonable cluster, take a larger framework
and put 27 habs into it in a 3 X 3 X 3 grid and you have a very large
cluster lots of mass, lots of people and perhaps with 10 million people per
habitat and say 3 of the habs used for recreation you have 240 million
people the equal of a nation the size of the USA. Of course there is nothing
to say that you have to have 10 million people in a habitat but even with
only 1 million per habitat you still have 24 million people, more than live
in Australia, where I live.

The question is how large can a cluster of habitats get before you would be
better starting a second cluster? Is there an optimum size for a cluster of
habitats after which you start to lose efficiency? Ignoring things like how
strong the frame can be, where are you going to get the mass and assuming
they do not need to be in direct sunlight, you have some other power source,
could you have a cluster with a million habitats or how about a billion?
What are the limits?

Darren