The study uses the Theory of Graphs in the implementation of bike lane in city with population between 70 and 100 thousand inhabitants, so that it is possible to calculate the shortest path between two vertices. The edges of this graph are the streets and avenues of the city. The process of choosing these streets is defined as Routing Problem in Arches based on the Smallest Path Problem can minimize costs, distances and path time. We conclude that graph theory has been successfully applied in a path defined with the aid of issues related to the graph.