  We perform a theoretical study, using {\it ab initio} total energy
density-functional calculations, of the effects of disorder on the $Mn-Mn$
exchange interactions for $Ga_{1-x}Mn_xAs$ diluted semiconductors. For a 128
atoms supercell, we consider a variety of configurations with 2, 3 and 4 Mn
atoms, which correspond to concentrations of 3.1%, 4.7%, and 6.3%,
respectively. In this way, the disorder is intrinsically considered in the
calculations. Using a Heisenberg Hamiltonian to map the magnetic excitations,
and {\it ab initio} total energy calculations, we obtain the effective $\JMn$,
from first ($n=1$) all the way up to sixth ($n=6$) neighbors. Calculated
results show a clear dependence in the magnitudes of the $\JMn$ with the Mn
concentration $x$. Also, configurational disorder and/or clustering effects
lead to large dispersions in the Mn-Mn exchange interactions, in the case of
fixed Mn concentration. Moreover, theoretical results for the ground-state
total energies for several configurations indicate the importance of a proper
consideration of disorder in treating temperature and annealing effects.
