Modeling an air route network structure with prefractal graphs
The paper highlights the main research areas: designing a network with given numerical characteristics, calculating the stability of a given network and a solution, solving optimization multicriteria problems with many parameters, and modeling dynamic networks. The structure of networks is hierarchical, with high clustering parameters; it has the properties of self-similarity at the global air transportation level. Air traffic networks are referred as scaleless networks or “small world” type. Their analysis involves using the theory of complex networks. The authors propose the apparatus of prefractal graphs as a tool for solving optimization problems. They also give basic definitions and notations, consider dynamic rules for generating graphs. In order to solve NP-complete problems in transport and logistics systems, it is proposed to use a method that reduces the complexity for a number of subtasks. The paper considers a model for covering an air route network with a prefractal graph, proposes to state a multicriteria problem of locating a multiple center with many weights, and gives a radial metric estimate. There is a proposed algorithm for placing a prefractal graph multiple center while maintaining the adjacency of old edges. Therefore, the authors generate a graph and select the multiple center vertices. The rules for generating a prefractal graph make it possible to generate networks with predetermined characteristics, such as vertex centrality, diameter, etc., including those for building air routes, locating airports and transfer hubs. The promising directions of further research are the recognition of real aircraft networks in the form of dynamic graphs, weighing by many weights and formulation of optimization multicriterial tasks, analyzing network structural characteristics, a statistical analysis based on small network structural elements, generating networks with specified properties and comparing them with real networks, analyzing structural stability of networks, etc.