  Let C be a clutter and let I be its edge ideal. We present a combinatorial
description of the minimal generators of the symbolic Rees algebra Rs(I) of I.
It is shown that the minimal generators of Rs(I) are in one to one
correspondence with the irreducible parallelizations of C. From our description
some major results on symbolic Rees algebras of perfect graphs and clutters
will follow. As a byproduct, we give a method, using Hilbert bases, to compute
all irreducible parallelizations of C along with all the corresponding vertex
covering numbers.
