Many graph algorithms are designed for imperative programming. It's safe to say that functional graph programming is still in its infancy. Alga[0], a system for algebraic graphs only came out in 2017. And efficient algorithms for graphs may yet to be discovered (even something as simple as reversing a list that's both efficient and elegant only came out in 1986!)
That said, as a beginner in functional programming, it would probably be good enough if you just focus on directly translating imperative graph algorithms to functional programming. You simply solve the problem by programming at a slightly lower level of abstraction.
I don't know if [0] would be any help, it doesn't talk about graphs in particular but does talk about functional-focused approaches to data structures. This note[1] on the wikipedia page for the book says it better than I could:
> [...] consider a function that accepts a mutable list, removes the first element from the list, and returns that element. In a purely functional setting, removing an element from the list produces a new and shorter list, but does not update the original one. In order to be useful, therefore, a purely functional version of this function is likely to have to return the new list along with the removed element. In the most general case, a program converted in this way must return the "state" or "store" of the program as an additional result from every function call. Such a program is said to be written in store-passing style.
Oh yeah, a pure function that accepts previous state, and returns the new state is the pattern I use a lot.
The issue is that it is hard to do on complex graph structures in an algorithm where incremental changes happen to the graph O(n) times - it ends up creating complex code and complex execution that might be slow to pass the time limit on Codeforces, let's say.
In the OCaml world maybe this is the place where you say "screw it, this abstracted function does some stateful temporary business, but it looks pure from the outside" but in Haskell it's a lot harder to pull off without going deep into monads (and I forget how those work every time).
Oh definitely go deep into monads. If you use the ST monad to do mutations, some people think Haskell provides nicer syntax to do imperative programming than traditional imperative languages like C. But of course such nicer syntax only comes from understanding and using important abstractions like monads, foldable, or traversable. Then there are niceties like automatic SoA/AoS transformation using type families.
Now if you understand the type family GHC extension, all this will be easily understood. If not, basically the idea is that you can automatically transform Array of Structs into Structs of Array by defining that transformation using a data family instance that you write yourself. For common types like tuples, the library already defined polymorphic instances for you.
Of course this transformation isn't always desirable and you don't have to use this. If your code isn't performance sensitive I wouldn't even bother with unboxed vectors; I'd just use regular vectors.
That said, as a beginner in functional programming, it would probably be good enough if you just focus on directly translating imperative graph algorithms to functional programming. You simply solve the problem by programming at a slightly lower level of abstraction.
[0]: https://dl.acm.org/authorize?N46678 or preprint at https://github.com/snowleopard/alga-paper/releases/download/...