Summary

A weighted_graph is a graph where each connection has a numeric edge_weight. Vertices are nodes in the network. It can be a directed_graph or an undirected_graph. Weights often model cost, distance, or time. The path_cost is the sum of edge_weight values along a path. Data structures include adjacency_list and adjacency_matrix with stored weights. Common goals are shortest_path and minimum_spanning_tree. Some graphs allow negative_weights, which affect algorithm choice.