Hi Bartmoss.
A couple of thoughts for you, take it or leave it if you like
Since we are largely talking about space territory, it is something that would be extraordinarily complex and might require some sort of three-dimensional representation. In addition, and taking the assumption that territorial soveriegnity is dependent upon the owner of the territory being able to respond against an 'invader' and employ deterence, the look of the territory itself might resemble a series of branches and arms depicting the points held by a territory (planet, solar system, asteroid, asteroid field) and the 'easiest' passage between those various points. The 'thickness' of that route would then be governed by the frequency that route is patrolled and the maximum range of the weapons systems designed. Sort of how the extent of a medieval city-state's territory can be given by how far their cavalry can reach within a day or so.
>looks back at rant, and scratches head<
Okay, I'm not sure if that is making any sense to anyone not me, so here's a map of the internet. The philosophy is the same - a 3D space, consisting of numerous points or nodes, and routes between them.
Is that better?
If not, I have a picture of a bunny with a pancake on it's head for those who don't know what I'm talking about!