Statistical characterization of a smallworld network applied to forest fires

Abstract

The characteristics of the propagation of forest fires under the influence of firebrands and the interaction zone (lx; ly) due to radiation are examined using the model of Small World Network. We analyze the distribution of the connections in a Small World Network and the cluster coefficient that represent the mathematical properties of the network. The used model is a stochastic model for predicting the behavior of wildfires. It is a variant of the social Small World Network, initially proposed byWatts and Strogatz, which allows the creation of more clusters and connections over long distances. This model was successfully applied to the spread of diseases and is characterized by a strong performance in clusters and a Poisson distribution of connections. The Model of Small World Network has also been adapted to study the spread of forest fires where it can include connections beyond nearest neighbors due to radiation from the flames or fire surges induced by firebrands which other propagation models cannot. It has been validated by experimental results of real fires. The main goal of this paper consists to investigate the most robust measures of network topology for a heterogeneous and=or homogeneous system near the percolation threshold.