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This article is focused on studying brachistochrone dynamic spaces of weakly connected graphs trough the example of Moscow transportation system. Research data will show and allow users to find the shortest route around the city, and give recommendations on the further development of the metropolis. The indicated dynamically changing contours of weakly connected graphs will allow the user to optimally adjust the traffic, which may ultimately result in new traffic capacity. Research results and conclusions may be useful for the Ministry of Transport, Traffic Management Centre, and private organizations.