A Vertex Elimination Algorithm for Enumerating all Simple Paths in a Graph | Zendy

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A Vertex Elimination Algorithm for Enumerating all Simple Paths in a Graph

Author(s) -

Fratta L.,

Montanari U.

Publication year - 1975

Publication title -

networks

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.977

H-Index - 64

eISSN - 1097-0037

pISSN - 0028-3045

DOI - 10.1002/net.1975.5.2.151

Subject(s) - vertex (graph theory) , algorithm , simple (philosophy) , matrix multiplication , inversion (geology) , mathematics , graph , simple algorithm , iterative method , matrix (chemical analysis) , computer science , fortran , combinatorics , materials science , epistemology , quantum mechanics , structural basin , composite material , quantum , paleontology , philosophy , physics , biology , thermodynamics , operating system

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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