Hi Stav - in order for Network to function, the curves have to be unwrappable to a regular 2D flattened grid. Think of this as similar to how a globe unwraps to lines of latitude and longitude on a flat map. All the lines of "latitude" must cross all the lines of "longitude", you can't have just separate little pieces of curves here and there that are not part of the regular grid layout.
Similarly if you've got a closed curve for one curve in one of the latitude or longitude lines, the other curves that are part of that direction of the grid must be closed as well.
So some of the things about your layout that breaks these requirements is you've got a closed curve here:
But then the other curve that should be a partner to that one (one of the same set of either longitude or latitude) is not closed, and does not cross the same extent of the other set of curves:
So you'd need to have a closed curve to match the other closed curve, then maybe once the network is complete you could slice off the end rather than trying to build to the sliced planar end directly in the network itself.
Also another problem is your curves are fragmented into little separate pieces instead of being all joined together into long segments to define full sections of the grid, like for example these little pieces are individually selectable:
One single line of "latitude" or "longitude" must be one long joined curve.
Check out some of these ring tutorials for some construction tips, these are from the Resources page on the wiki:
