In graph theory, a weighted edge is an edge that has a numerical value, or weight, assigned to it. This weight can represent various factors, such as distance, cost, or time, depending on the context of the graph. Weighted edges help in analyzing and solving problems related to networks, such as finding the shortest path or minimizing costs. Weighted edges are commonly used in algorithms like Dijkstra's algorithm and the A* search algorithm. These algorithms utilize the weights to determine the most efficient route through a graph, making them essential in applications like navigation systems and network routing.