How to get the shortest path between two points on Google maps

I don't know if this is Google's proprietary thing or its open source. I need to know how Google shows different routes, as well as the shortest of them based on the available road . Because I created a Google map application where the user can place a marker and thus get the simplest (shortest in my sense) destination with accessible roads (not just a line as this Q shows ( Google MAP API: how to draw the shortest path between two geographical points?

I know this applies to Dijkstra's algorithm for the shortest path. but I was wondering if there is any library that I can use out of the box.

Thank,