• Symmetric directed graphs are directed graphs where all edges are bi-directional. This means, for every arrow that belongs to the digraph, the corresponding inverse arrow also belongs to it.
• Simple directed graphs are directed graphs that have no loops, arrows that directly connect vertices to themselves, and no multiple arrows with same source and target nodes. As already introduced, in case of multiple arrows the entity is usually addressed as directed multigraph. Some authors describe digraphs with loops as loop-digraphs.
• Complete directed graphs are simple directed graphs where each pair of vertices is joined by a symmetric pair of directed arrows; equivalent to an uni-directional complete graph with the edges replaced by pairs of inverse arrows. It follows that a complete digraph is symmetric.
• Oriented graphs are directed graphs having no bidirectional edges; i.e. at most one of (x, y) and (y, x) may be arrows of the graph. It follows that a directed graph is an oriented graph if and only if it hasn’t any 2-cycle.
• Directed acyclic graphs (DAGs) are directed graphs with no directed cycles.
• Multitrees are DAGs in which no two distinct directed paths from a single starting vertex meet back at the same ending vertex.
• Oriented trees or polytrees are DAGs formed by orienting the edges of undirected acyclic graphs.
• Rooted trees are oriented trees in which all edges of the underlying undirected tree are directed either away from or towards the root.
In other words, a directed graph vs. a directed acyclic graph are described
in graph theory as shown above: AGF, CE, HAB are directed graphs, while BCDEF, DGH are directed acyclic graphs (DAGs). Software flow diagrams may take either directed graph form. If a symmetric directed graph, then the return edge or transition may be a return req/ack, for example. If a non symmetric directed graph, most common; then might be a simple directed graph, or an acyclic directed graph. Directed acyclic graphs with loops may be more efficient than directed graphs, where extra states may precede an equivalent loop. Graph, or task graph, theory can be abstract when minimizing the vertices (states), or edges (transitions).
Web: https://en.wikipedia.org/wiki/Directed_graph