Search for shortest paths based on the projective description of unweighted graphs

A new method of representing graph projections in computer memory is proposed, which is more informative than matrix and list data structures based on elementary relations of vertices adjacency or edge incidences. The class of graphs considered in this study is expanded to include mixed graphs containing both undirected and directed edges (arcs). A new method for searching the shortest routes based on this approach is also proposed. The results of the general and special (for compact graphs) analysis of the asymptotic complexity of this method in solving typical SPP problems (Shortest Path Problem) show that the developed method is highly efficient and will find its application not only in information networks, where there are particularly high requirements for the topology of computing systems and the efficiency of finding shortest routes, but also in other scientific, technical, transport and economic fields.