On balanced cuts of graphs in metric spaces

The report focuses on the description of the method of constructing an approximate solution of the problem of cutting a graph whose vertices represent points in a metric space and edges are equipped with two numeric attributes: distance between the terminal vertices and the strength of the connection between these vertices. It is required for a given number k to construct k subgraphs in the original graph such that, firstly, the subgraphs are connected, the sets of their vertices are pairwise disjoint and the union of these sets coincides with the set of vertices of the original graph; secondly, the number of vertices in the subgraphs is approximately the same; thirdly, the total magnitude of the binding forces between different subgraphs was minimal. The results of applying the proposed method to the problem of cutting a railway network are presented.