Discrete q-Green potentials related to the equation Δu􀀀qu = 0 on an innite network were studied in [12] as a discrete analogue to [9]. We study some properties of q-Green potentials with nite q-Green energy. The q-Dirichlet energy plays an important role instead of the Dirichlet sum. Our aim is to show that results obtained in [7] in case q = 0 hold similarly even in case q  0. We show that every q-Dirichlet potential can be expressed as a difference of two q-Green potentials with nite q-Green energy.