How to go about pathfinding based on custom placed nodes?

I'm trying to make a point and click type adventure game, and the system I want to use to make the player navigate the world would be based on nodes which I manually place. This system is basically how navigation in Sword & Sworcery worked (I'm pretty sure).

Basically the system I want to implement is one where each node is connected to certain other nodes, meaning that when the player is on that node, they will only be able to move to whatever nodes are connected to it. All of these nodes will be connected forming a web-like path on each level, where the player can only travel between nodes that I allow.

I looked up pathfinding, and almost all of the results are tile based, but I don't really think that would be of much help with the system I have in mind, although I could be wrong.

Any help or resources would be greatly appreciated.