Abstract. If G is a graph, then its path graph, P_k(G), has vertex set identical with the set of paths of length k in G, with two vertices adjacent in P_k(G) if and only if the corresponding paths are "consecutive" in G. If we replace the term "path" by "trail" ("walk"), we obtain trail graph T_k(G) (walk graph W_k(G)). Path graphs are generalization of line graphs, as well as trail and walk graphs. Obviously, the path graph P_k(G) is an induced subgraph of the trail graph T_k(G), which is an induced subgraph of the walk graph W_k(G). We prove that the walk graph W_k(G) is an induced subgraph of the k-iterated line graph L^k(G), using a special embedding preserving histories. Hence, trail and walk graphs are in a sense more close to line graphs, and some problems that are compliacted for path fraphs may be easier for walk graphs.