(def graph
  {"a" {:dependencies ["b" "d"]}
   "b" {:dependencies ["c" "e"]}
   "c" {:dependencies ["d" "e"]}
   "d" {:dependencies []}
   "e" {:dependencies []}})

(defn resolve-dep
  [graph name]
  (let [resolved (atom [])
        resolved-set (atom #{})
        f (fn f [name]
            (doseq [x (:dependencies (graph name))]
              (f x))
            (when-not (@resolved-set name)
              (swap! resolved conj name)
              (swap! resolved-set conj name)))]
    (f name)
    @resolved))

(resolve-dep graph "a")
;=> ["d" "e" "c" "b" "a"]

This code works, but not sure if it's idiomatic clojure code.
The use of atom feels like procedural than functional to me since
there's no concurrency involved at all.

Any suggestions?

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