  We formulate a simple model for the bounded derived category of gentle
algebras in terms of marked ribbon graphs and their walks, in order to analyze
indecomposable objects, Auslander-Reiten triangles and homological bilinear
forms, and to provide some relevant derived invariants in a graph theoretic
setting. Among others, we exhibit the non-negativity and Dynkin type of the
homological quadratic form of a gentle algebra, describe its roots as the
classes of indecomposable perfect complexes in the Grothendieck group, and
express its Coxeter polynomial in terms of the Avella-Alaminos Geiss invariant.
We also derive some consequences for Brauer graph algebras.
