Data Structures Questions Medium
A weighted graph is a type of graph where each edge is assigned a numerical value called a weight. The weight represents the cost, distance, or any other relevant metric associated with traversing that edge.
In a weighted graph, the weights can be positive, negative, or zero. Positive weights typically represent distances or costs, while negative weights can indicate benefits or advantages. Zero weights are often used to represent a direct connection or absence of a cost.
To work with a weighted graph, various algorithms and techniques can be applied. For example, the shortest path algorithm, such as Dijkstra's algorithm or Bellman-Ford algorithm, can be used to find the path with the minimum total weight between two vertices. Minimum spanning tree algorithms, like Prim's algorithm or Kruskal's algorithm, can be used to find the tree that connects all vertices with the minimum total weight.
Weighted graphs are commonly used in various applications, such as network routing, transportation planning, scheduling, and optimization problems. By assigning weights to the edges, these graphs provide a way to model and solve real-world problems that involve considering the costs or distances associated with different paths or connections.