Spatial Growth Models with Random Node Failures

Ad-hoc network is an important applied branch of scale-free networks, which has been widely studied. In this paper, insertions and failures of nodes in ad-hoc networks are modeled in spatial growth models. The preferential attachment probability is based on the topological degree and modulated by a Euclidean distance dependent power-law function. Node failures are represented by random node deletions in the model. Degree distributions of the proposed spatial growth models for ad-hoc networks are evaluated. The results show that both the Euclidean distance dependent preferential attachment and the random node deletion can change the degree distribution. When the distance exponent is smaller than-1 or the deletion ratio is larger than 0.5, the network is not scale-free any more, and the degree distribution follows the exponential decay law. The varying of the average degree of the node with time is also evaluated. The results show that, irrelevant to the distance exponent, the average degree can achieve a convergent value for each value of the deletion ratio and simulation results match calculated values completely.