  Studying network robustness for wireless sensor networks(WSNs) is an exciting
topic of research as sensor nodes often fail due to hardware degradation,
resource constraints, and environmental changes. The application of spectral
graph theory to networked systems has generated several important results.
However, previous research has often failed to consider the network parameters,
which is crucial to study the real network applications. Network criticality is
one of the effective metrics to quantify the network robustness against such
failures and attacks. In this work, we derive the exact formulas of network
criticality for WSNs using r-nearest neighbor networks and we show the effect
of nearest neighbors and network dimension on robustness using analytical and
numerical evaluations. Furthermore, we also show how symmetric and static
approximations can wrongly designate the network robustness when implemented to
WSNs.
