Final answer:
A weighted graph is a type of graph used in many applications where edges have weights representing costs, such as distance or time, affecting the total cost of a path.
Step-by-step explanation:
A weighted graph is a special type of graph where each of the edges is assigned a weight. The weight is associated with a cost for using that edge to move from one node to another. In such graphs, weights might represent distance, cost, or any other factor that must be minimized or maximized during pathfinding or network optimization problems. Weighted graphs are commonly used in various applications like finding the shortest path in navigation systems, optimizing network routing, and scheduling problems.
In a weighted graph, the weights can be represented as numbers on the edges, and any path through the graph will have an overall cost, which is the sum of the weights of the edges that make up the path. Different algorithms such as Dijkstra's algorithm or the A* search algorithm are used to find the shortest path between nodes in a weighted graph.