Nodes and graphs. How to implement?

Hello! I need to create a sequence of nodes / graphs, so that the character can move on the roads. We have a neighbor node and the player can move only to the neighboring node.

Advise how best to implement it by means of a Tiled.

Thank you and sorry for bad english.

You can:
Enumerate all possibilities of connections (road) and draw them down as tile images.
Create a new layer and place your road tiles.
Map every kind of tiles with correct connectivity in code.

I’d just add, that since you’ve already got your road tiles, you could associate a custom property with each road tile telling your engine how it connects to its neighbors. That way you don’t need to do any additional work for this, apart from assigning those properties once.

If you then save the tileset as an external tileset, you can share those annotated tiles between multiple maps.