Abstract
If a suitable definition of sum and multiplication between sets of paths is given, the sets of all simple paths between all pairs of vertices in a graph can be characterized as the solution of a system of linear equations. The well‐known matrix technique for enumerating such paths corresponds to an iterative solution of this system. A new and more efficient algorithm is here described and analyzed which finds all simple paths by a vertex elimination technique similar to Jordan's method for matrix inversion. Experimental results about a FORTRAN implementation of the algorithm are finally reported.
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