# Predicting and Modeling Wildfire Propagation Areas with BAT and Maximum-State PageRank
## 1 Introduction  
The network research is very popular and has been applied to research in many fields [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. Recently, wildfires have seen unbelievable growth in size, frequency, and complexity. As defined in [28], wildfire is a non-structure and non-prescribed that occurs in wildlands. Wildfires often ignite close to wildland-human boundaries, resulting in severe damage to assets [28; 29; 30], air pollution [31; 32], loss of plants and forest [33; 34; 35], and high fatalities [36; 37]. With global warming, a \(1^{o}\) increase in the climatic temperatures causes a 15% growth in wildfires [38]; the wildfires in turn increase the temperature, thereby further increasing the number of wildfires, forming an infinite loop [28; 38]. Wildfire is a severe practical problem [28; 38], and does not always occur in the same area, such as a town or city, but expands to the neighboring areas, and is affected by weather conditions, e.g., wind, rain, etc., and location surface, such as forest or lake [36]. Hence, unlike the traditional path problem [39], which states that all events occur in a path, and the spanning tree problem [40], which has fixed destinations, the wildland fire problem requires a new algorithm to estimate its occurrence and the possible results of its propagation [32; 33; 34]. Several deterministic and probabilistic models have been proposed to predict the wildfire propagation from node-to-node (cell/city/area) [28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. Among them, graph-based methodologies,including the path-based and tree-based methodologies, are popular [32; 33; 34]. Furthermore, many probabilistic wildfire propagation models have been proposed based on the continuous-time Markov chain [41]. The path-based algorithms [32; 33; 34] focus on identifying the deterministic or stochastic paths with the shortest distance, minimal travel time, or high probability. The tree-based algorithms emphasize on one-source to many-targets and one ignition to many different and known nodes, rather than the one-source to one-target, i.e., from ignition to another target, which is the basis of path-based algorithms [39; 40]. The tree-based algorithms include all cellular automata-related algorithms. Furthermore, the path-based and tree-based algorithms require the final destination information [32; 33; 34; 39; 40]. Free-burning wildfire propagation exhibits extremely inconstant and chaotic behaviors [32; 35; 41]. In this study, we demonstrate that the wildfire propagations can be modeled as a scale-free network [42; 43], which is a common and effective method to depict complex systems. To the best of our knowledge, this is the first time that the wildfire propagations are modeled as scale-free networks among the existing literature. Many practical and important networks are scale-free networks where the node degree [42; 43; 44; 45], i.e., the number of edges connected to a node, follows an asymptotical power-law distribution [44]. A model of the scale-free network is a scale-free model [42]. Several examples of the study and use of scale-free networks are available and include the sharing of information among nodes in the network via links, such as the world wide web, protein-interaction networks, metabolic networks for eukaryotes and bacteria, co-authorship/collaborative network, and power grid of the western United States [42; 43; 44; 45]. Among the different models of scale-free [45] networks, the Barabasi-Albert model [45] is the most popular with numerous variations and generalizations [45]. Hence, the Barabasi-Albert model is used to model the propagation characteristic property of the wildland fire and generate test data to validate the performance of the proposed algorithm.