Istituto di Scienza e Tecnologie dell'Informazione     
Montanari U., Fratta L. All simple paths in a graph by solving a system of linear equations. Internal note IEI-B71-11, 1971.
If a suitable definition of sum and multiplication is given, the problem of finding all simple paths between each pair of vertices in a graph can be stated as a system of linear equations. The well-known matrix tecnique corresponds to an iterative solution to this system. Gaussian elimination, however, gives a new and very promising approach.

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