The topology of a sensor network changes very frequently due to node failures because of power constraints or physical destruction. Robustness to topology changes is one of the important design factors of wireless sensor networks which makes them suitable to military, communications, health and surveillance applications. Network criticality is a measure which capture the properties of network robustness to environmental changes. In this work, we derived the analytical formulas for network criticality, normalized network criticality and studied the network robustness for r-nearest neighbor cycle and r-nearest neighbor torus networks. Further, we compared our analytical results with simulation results and studied the effect of number of nodes, nearest neighbors and network dimension on the network criticality and normalized network criticality.

翻译：由于电源限制或物理破坏造成的节点失灵,传感器网络的地形变化非常频繁。对地形变化的强烈性是无线传感器网络的重要设计因素之一,使得这些网络适合军事、通信、健康和监视应用。网络临界性是测量网络对环境变化的稳健性特性的一个尺度。在这项工作中,我们得出网络临界性、网络正常度的分析公式,并研究了网络对近邻和近邻网络的稳健性。此外,我们将我们的分析结果与模拟结果进行比较,并研究了节点、近邻和网络层面对网络临界性和正常度的影响。