Abstract: A method of computing shortest paths in a weighted graph having vertices and an adjacency matrix with memory resources and a processor including (a) selecting integer weights; (b) carrying out a series of incrementations, an incrementation including finding a set of vertices to which one may arrive from a given set of vertices; (c) carrying out a series of decrementations, a decrementation including finding a set of vertices from which one may go to arrive to a given set of vertices; (d) causing the incrementations and decrementations to be carried out in any order; (e) transforming vectors of increments/decrements in paths, the paths making up a set E1 of the shortest paths in term of number of arcs or using a given number of arcs, Na; (f) selecting n-uple of paths C of lowest cost among set of paths E1; (g) calculating Nb=Na+1; (h) computing iteratively, while Nb≦W(C) the following steps: i.