Node Navigation for NPCs (Platformer)

How would I go about having NPCs follow a path of nodes to head towards any specified object, such as a Zombie following nodes to reach a Player.

Example of what I am talking about:

<img src="http://img856.imageshack.us/img856/8458/nodeexample.png">

[Image too large. click "View Image" to get the whole thing]

Squares = nodes

Star = Player/Goal

Diamond = NPC

The NPC would automatically detect if there is a wall he can jump over, or if there is a ledge he can jump up too.

Is this possible in Construct, or is there a better way?

Yup, that's possible. I saw a similar cap somewhere using the platform behaviour to do this (as platform behaviour has the conditions "wall on left" and "wall on right")

Not sure if it's the best way to do it, but I'd do something similar if I was making a platformer.