Is posible to prove if the subway routes in a city were made using the graph theory? How?

No.

Step-by-step explanation:

Unless the design notes are archived, in our current reality, it is not possible to prove that a designer used any particular theory in the design of anything. Such a proof would involve after-the-fact mind-reading.

Even with design notes in hand, it is unlikely you could prove the designer was cognizant of any particular theory when writing the notes. All the time, people write things they don't understand, or that have meaning that is understood only after some time.