The algorithms to solve shortest paths in weight graphs with matrix methods

AimSome algorithms to find the shortest paths in weighted graphs are studied.MethodsBased on the matrix calculation,the algorithms are presented.ResultsThe algorithms include the follows: the algorithm to find the shortest path between any pairs of nodes;the algorithm to find the shortest path between any pairs of nodes under the condition of the shortest path including minimum edges; the algorithm to find all shortest paths between any pairs of nodes;and the algorithm to find the N shortest paths between any pairs of nodes.ConclusionBecause the algorithms in the paper use the matrix as the tools, the design of the program is easy. Validation of the algorithm is proved in practices.