A weighted graph is a type of graph where each edge has a numerical value associated with it, known as a weight. This weight represents the cost or distance between two vertices in the graph.
A weighted graph can be represented using an adjacency matrix or an adjacency list. In an adjacency matrix, the weights are stored in a matrix format where rows and columns represent the vertices. In an adjacency list, the weights are stored as a list of edges and their corresponding weights.
The weights in a graph can represent various real-world scenarios, such as the cost of traveling between cities or the distance between two locations. They can also be used in algorithms to find the shortest path or minimum spanning tree in a graph.
To find the shortest path in a weighted graph, you can use algorithms such as Dijkstra's algorithm or the Bellman-Ford algorithm. These algorithms take into account the weights of the edges and find the shortest path between two vertices in the graph.
Yes, a weighted graph can have negative weights. However, it can cause issues with certain algorithms, such as Dijkstra's algorithm, as it assumes all edge weights are positive. In such cases, other algorithms like the Bellman-Ford algorithm can be used instead.