Forest fire on a configuration graph with random fire propagation

The paper considers a random process of fire propagation over links of two types of configuration graphs with random node degrees. Node degrees follow either a power law or the Poisson distribution. The process takes place in a random environment where the probabilities of fire propagation follow the standard uniform distribution. The optimal values of the node degree distribution parameters that ensure maximum node survival in case of a fire were estimated. The results were obtained for two cases of fire start: targeted start — when a fire starts from the node with the highest degree and random ignition — when a fire starts from an equiprobably chosen node. A comparative analysis of two graph models (power law and Poisson) in terms of the number of nodes remained after the fire was performed.