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We study modular and integral flow polynomials of graphs by means of subgrouparrangements and lattice polytopes. We introduce an Eulerian equivalencerelation on orientations, flow arrangements, and flow polytopes; and we applythe theory of Ehrhart polynomials to obtain properties of modular and integralflow polynomials. The emphasis is on the geometrical treatment through subgrouparrangements and Ehrhart polynomials. Such viewpoint leads to a reciprocity lawfor the modular flow polynomial, which gives rise to an interpretation on thevalues of the modular flow polynomial at negative integers, and answers aquestion by Beck and Zaslavsky.

Orientations, lattice polytopes, and group arrangements II: Modular and integral flow polynomials of graphs