  Numerical calculations of the average dipole-coupling energy $\bar
E_\mathrm{dip}$ in two-dimensional disordered magnetic nanostructures are
performed as function of the particle coverage $C$. We observe that $\bar
E_\mathrm{dip}$ scales as $\bar E_\mathrm{dip}\propto C^{\alpha^*}$ with an
unusually small exponent $\alpha^*\simeq 0.8$--1.0 for coverages
$C\lesssim20%$. This behavior is shown to be primarly given by the
contributions of particle pairs at short distances, which is intrinsically
related to the presence of an appreciable degree of disorder. The value of
$\alpha^*$ is found to be sensitive to the magnetic arrangement within the
nanostructure and to the degree of disorder. For large coverages $C\gtrsim20%$
we obtain $\bar E_\mathrm{dip}\propto C^\alpha$ with $\alpha=3/2$, in agreement
with the straighforward scaling of the dipole coupling as in a periodic
particle setup. Taking into account the effect of single-particle anisotropies,
we show that the scaling exponent can be used as a criterion to distinguish
between weakly interacting ($\alpha^* \simeq 1.0$) and strongly interacting
($\alpha^* \simeq 0.8$) particle ensembles as function of coverage.
