Let G be a directed multigraph, and let H be the induced directed graph whose vertices are the edges of G, and whose edges are given by pairs of consecutive edges in G; i.e., there is an edge from v to w in H if and only if the terminal vertex of v in G is the initial vertex of w. In the case where G has no extremal vertices, is G recoverable from H? If so, is there an equivalence of categories between directed multigraphs without extremal vertices and directed graphs without extremal vertices, given by forming the induced graph?
