The all-pairs shortest path problem is the determination of the shortest graph distances between every pair of vertices in a given graph. The problem can be
solved using
applications of Dijkstra's algorithm or all
at once using the Floyd-Warshall algorithm.
The latter algorithm also works in the case of a weighted graph where the edges have
negative weights.
The matrix of all distances between pairs of vertices is called the graph
distance matrix, or sometimes the all-pairs shortest path matrix.
applications of Dijkstra's algorithm or all
at once using the Floyd-Warshall algorithm.
The latter algorithm also works in the case of a weighted graph where the edges have
negative weights.
can be found in the Wolfram
Language using GraphDistanceMatrix[g],
and a shortest path between two vertices 
and 
using FindShortestPath[g,
u, v].
