# Two basic graph operations?

I have recently read in a text by Didier Caucal that a graph has two basic operations, namely, unfolding and path function.

I have some questions:

Does the path function correspond to what Feynman called the path integral? If not, how would you describe it?

Does unfolding have to do with the way the seed of a function develops?

Could you provide reasonable and intuitive illustrations for both operations?

And finally (and somewhat unrelated, is one represented a certain types and sets of morphisms as transformations, can those be derived from properties of the graph? If so, how exactly?