Zoning of districts of the region according to the proximity to the external border

A map of a certain region with marked areas is considered. Zoning of map areas is carried out according to their proximity to the borders of the region. An algorithm for hierarchical classification of map regions is constructed, as a result of which they are divided according to the degree of their distance from the regional border. The shortest paths from various areas to the regional border are determined. In this case, the path length refers to the number of inter-district boundaries that the path crosses. The basis of these constructions is the definition of a dual to a planar graph depicting a map of the region. As an example, we consider a map of the administrative districts of Primorsky Krai, in which the districts are colored according to their proximity to the land border of the region.