  The effects of magnetic dilution and applied pressure on frustrated spinel
Ni$_{2-x}$Mg$_{x}$GeO$_{4}$ (0 $\leq x \leq 1.0$) are analyzed using specific
heat, AC and DC magnetization and x-ray diffraction. The parent compound has
two closely spaced antiferromagnetic transitions $T_{\text{N1}}=12.0$ K
(kagom\'e planes) and $T_{\text{N2}}=11.4$ K (triangular planes). In the
dilution range tested, the low temperature magnetic state takes three forms:
antiferromagnetic ($0 \leq x \leq 0.05$), ill-defined ($x=0.10$ and 0.15), and
spin glass ($0.30 \leq x \leq 1.0$). The AFM region shows an extreme
vulnerability to dilution with a percolation threshold of $p_{\text{c1}}=0.74
\pm 0.04$ and $p_{\text{c2}}=0.65 \pm 0.05$ for the kagom\'e and triangular
planes respectively, which are much larger than expected for 3D systems. We
suggest that this behavior is possibly due to coupling between the kagom\'e and
triangular spins forming a 'network of networks' (NON). Thermal expansion data
on parent NGO indicates a field dependent lattice contraction during ordering
events. Furthermore, there is a transition from contraction to expansion in an
applied field of 6 T in the kagom\'e planes. For dilution levels $x \geq 0.30$,
the system becomes a spin glass with canonical behavior. Specific heat results
suggest that the triangular spins become disordered with increasing Mg$^{2+}$
substitution followed by the onset of glassiness in the kagom\'e planes.
Furthermore, there appears to be a dilution driven shift from 3 dimensional to
2 dimensional behavior as the low temperature magnetic heat capacity scales as
$T^{2}$ in the spin glass state.
