  A path graph is the intersection graph of paths in a tree. A directed path
graph is the intersection graph of paths in a directed tree. Even if path
graphs and directed path graphs are characterized very similarly, their
recognition algorithms differ widely. We further unify these two graph classes
by presenting the first recognition algorithm for both path graphs and directed
path graphs. We deeply use a recent characterization of path graphs, and we
extend it to directed path graphs. Our algorithm does not require complex data
structures and has an easy and intuitive implementation, simplifying
recognition algorithms for both graph classes.
