Elements of the theory of matroids and graph theory lie at the heart of many network models of the economy. The authors consider the problems of introduction of an effective scheme for one-way traffic on the streets and optimal placement of the connecting elements to the square planar frameworks for their rigidity. They proposed algorithms for solving these problems, based on the necessary and sufficient conditions for strong connectivity of the digraph, algorithms for constructing spanning trees of minimal weight or shortest distances, as well as methods for finding centers and medians in network.
Keywords: mathematical model; economic system; matroid; greedy algorithm; strongly connected graph; spanning tree; planar square framework rigidity.
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https://doi.org/10.24151/2409-1073-2018-4-36-40