Understanding data-flows graph
Being acyclic is inferred because it has leaves, which by definition do not cycle or loop back to a previous node. Think of the data flow as being like the transport of water through a tree. It starts at the root, goes up through the branches (which may grow into each other) and finally to the leaves where it evaporates into the atmosphere. Once it gets to the leaves it's done, and cannot loop back to form cycles.    

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  "A graph with no cycles is called an acyclic graph. A tree is a
  connected acyclic graph. A rooted tree is a tree with a distinguished
  vertex, called a root. Vertices of a tree are also called  nodes. In
  addition, they are called leaves when they are adjacent to only
  one vertex each".


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  "Let us consider first a sequencing graph entity that has only
  operation vertices, e.g., a non-hierarchical model or an entity that
  is a leaf of the hierarchy. The vertex set V is in one-to-one
  correspondence with the operations. The edge set E models the
  dependencies due to data flow or serialization. The graph has two
  major properties. First, it is acyclic..."


Directed Acyclic Graph