Hi BlackBird - network needs to have an overall rectangular topology to it. It can be bendy but it can't have things like multiple branches in it because multiple branches like that do not map down to a 2 dimensional UV grid, and makings map to a 2D UV grid is one of the things that Network requires.

Think of Network being sort of like mapping latitude and longitude lines on a map of the world on to a globe - the latitude and longitude lines on the 2D map are the UV grid, and the globe is the 3D curves.

Your branching structure there does not unwrap to a UV grid so it is not suitable for doing all in one single big network.

When that happens, it means that you are trying to build too much all in one single surface - instead you've got to build your model out of multiple different parts and them combine those parts together.

For something like you are showing there, you'll probably want to build 2 tubes and then slice them up and put a blend between them, see Mike's previous post here for an example:
http://moi3d.com/forum/index.php?webtag=MOI&msg=4388.55

But basically you've got to divide things up more - you're trying to do too much variation within a single Network pass - an individual Network can only construct one regular shaped surface, if you need irregularity then you need to split it up into multiple pieces.

- Michael