  We classify graded Hopf algebras structures over path coalgebras, that is
over free pointed coalgebras, using Hopf quivers which are analogous to Cayley
graphs.
  The description involves formulas for the product besides the canonical
formulas for the coproduct. This makes explicit the quantum shuffle product
making use of natural elements in a Hopf bimodule having a simple "geometrical"
interpretation in the quiver sense, rather than working systematically with
right or left coinvariants.
