A weighted graph is a type of graph in which each edge has a numerical value, known as a weight, associated with it. These weights can represent various metrics, such as distance, cost, or time, depending on the context of the graph. The weights allow for more complex analysis and decision-making, as they provide additional information about the relationships between the vertices. In a weighted graph, the vertices are connected by edges, and the weight of an edge indicates the strength or cost of the connection. This makes weighted graphs useful in many applications, such as network routing, transportation planning, and social network analysis, where understanding the significance of connections is crucial.