It depends on the city itself, though larger cities tend to have more connections. Pella, for example, has 16 land connections (in Hegemony Gold), while Aegeae has only 3. For coastal cities, it's split between naval and land connections, and you can physically see the number. Land connections are little market stalls outside the city walls, and naval connections are docks. In the pop-up menu for each city when you move your cursor over them, the last number is the number of used connections versus the total number of connections.
To delete a supply line, click on it, then click the delete button.