  This is the first one of a series of papers on association of orientations,
lattice polytopes, and abelian group arrangements to graphs. The purpose is to
interpret the integral and modular tension polynomials of graphs at zero and
negative integers. The whole exposition is put under the framework of subgroup
arrangements and the application of Ehrhart polynomials. Such viewpoint leads
to the following main results of the paper: (i) the reciprocity law for
integral tension polynomials; (ii) the reciprocity law for modular tension
polynomials; and (iii) a new interpretation for the value of the Tutte
polynomial $T(G;x,y)$ of a graph $G$ at $(1,0)$ as the number of
cut-equivalence classes of acyclic orientations on $G$.
