A Study on the Robustness and Fragility of Tree-Based Wireless Sensor Networks with Community Characteristics

A number of recent studies have concentrated on the statistical properties of large-scale tree based wireless sensor network with community characteristics. The robustness and fragility of wireless sensor networks, whose underlying architecture patterns crucially affect the system functionality, is defined as the resilience to deletion of network nodes, which is equivalent to be a percolation model on a graph depicting the network. In this paper we have derived an analytic solution of the site percolation model using generating function formalism on a Cayley-Tree based wireless sensor network structure with community features. Our solution provides predictions for quantities including the position of the percolation threshold and the average cluster size as functions of rewiring probabilities and occupation proportion respectively. All the analytic results show great agreement with their extensive numerical simulations counterparts.