How to correctly present a map (metro) for search and what algorithm to implement?

Question

Java

I am implementing a mobile application map of the metro. Faced a search problem, which should pave the route from station to station.

Answer 1

Finding a path in a graph.
But, given the number of stations, it is easier to prescribe all the routes in advance, there are only 15 of them.

Answer 2

And they also argue whether a programmer needs mathematics ...
According to the link, the theory, I think it will not be difficult to code something like that.

Answer 3

Neo4j is an open source graph database management system implemented in Java.