Here's a quick image:
I've generated a navmesh for my game that shows how an AI can get to each of its possible neighboring tiles in a map. (I followed some gamasutra article as reference, I'll paste a link if I can find it again). You can see that it calculates all possible jump, fall, and walking connections between points.
Now that I have this, I've been researching how to actually use it. I understand that A* is generally the algorithm that people use but I haven't been able to find a resource for adapting it to a non-grid based dataset. Any articles that you know of or pseudocode would be awesome :)