Linked from
The 12 pages that link to Weighted graph, each with the reason it gives.
Shortest path problemRelated: Its edge weights supply the quantities summed along candidate paths.
Edge (graph theory)Broader topic: An edge weight adds quantitative information to the connection.
Dijkstra's algorithmRelated: The algorithm compares sums of edge weights to rank paths.
Bellman–Ford algorithmRelated: Those weights determine the path costs Bellman–Ford compares.
Laplacian matrixRelated: Edge weights replace binary adjacency values in weighted Laplacians.