  Disordered complex networks are of fundamental interest as stochastic models
for information transmission over wireless networks. Well-known networks based
on the Poisson point process model have limitations vis-a-vis network
efficiency, whereas strongly correlated alternatives, such as those based on
random matrix spectra (RMT), have tractability and robustness issues. In this
work, we demonstrate that network models based on random perturbations of
Euclidean lattices interpolate between Poisson and rigidly structured networks,
and allow us to achieve the best of both worlds : significantly improve upon
the Poisson model in terms of network efficacy measured by the Signal to
Interference plus Noise Ratio (abbrv. SINR) and the related concept of coverage
probabilities, at the same time retaining a considerable measure of
mathematical and computational simplicity and robustness to erasure and noise.
  We investigate the optimal choice of the base lattice in this model,
connecting it to the celebrated problem optimality of Euclidean lattices with
respect to the Epstein Zeta function, which is in turn related to notions of
lattice energy. This leads us to the choice of the triangular lattice in 2D and
face centered cubic lattice in 3D. We demonstrate that the coverage probability
decreases with increasing strength of perturbation, eventually converging to
that of the Poisson network. In the regime of low disorder, we approximately
characterize the statistical law of the coverage function.
  In 2D, we determine the disorder strength at which the PTL and the RMT
networks are the closest measured by comparing their network topologies via a
comparison of their Persistence Diagrams . We demonstrate that the PTL network
at this disorder strength can be taken to be an effective substitute for the
RMT network model, while at the same time offering the advantages of greater
tractability.
