image updated to include Sandlapper's better idea about displaying blockades.
In this example Red and Yellow are allied, and Red is at war with Teal. This sort of display is intended as normal, and in-fact is quite close to what the game currently does. It could be applied to various proposals.
* Solid colored SLs: Standard supply routes between colonies
* Parallel striped colored SLs: A Standard supply route shared by 2 empires. I.e. both have colonies at both ends. (Olympus to Vindemiatrix)
* SL colored differently at each end: Supply lines connecting allies. (Graffias to Asterope)
* Grey SLs: SLs not used as supply lines.
* Dotted line: A Military supply line, connecting to ships beyond standard routes.
* If the alliance between Yellow and Red were ended, but they didn't go to war, the Graffias-Asterope line would be broken, while Olympus-Vindemiatrix would remain active.
* Red has blockaded Teal's Dnoces. Notice that no supply lines go to it, in spite of all the adjacent colonies.
* The fleet at Cannon has 3 Red colonies at 2 SLJs away. Presumably supplies could be coming from any of those three. But if supply line cutting is going to be an important part of the game, those lines should be visible. But if this line were cut, i suppose it would jump to Kilja or Arneb. I rather dislike the idea of manually creating Military supply lines. (Also applies to fuel routes for non-combat scouts, colony ships) If one is possible, i believe the optimal line should create itself. Such automatic military supply line would be a little harder to block by the enemy, but saves the uninteresting micro of defining throw-away supply routes.
A bit of progress toward this has happened, as seen below: