WeightedAdjacencyGraph
WeightedAdjacencyGraph[wmat] gives the graph with weighted adjacency matrix wmat.
WeightedAdjacencyGraph[{v1, v2, ...}, wmat]gives the graph with vertices vi and weighted adjacency matrix wmat.
Examples
Create a weighted graph from a matrix:
WeightedAdjacencyGraph[{{0, 1, 2}, {1, 0, 3}, {2, 3, 0}}]With named vertices:
WeightedAdjacencyGraph[{"A", "B", "C"}, {{0, 5, 0}, {5, 0, 3}, {0, 3, 0}}]Please visit the official Wolfram Language Reference for more details.