Weighted Graph
A weighted graph is a graph data structure where edges have associated numerical values called weights, representing costs, distances, capacities, or other metrics. It extends basic graph theory by adding quantitative information to connections between vertices, enabling modeling of real-world scenarios like network routing, resource allocation, or optimization problems. Common algorithms for weighted graphs include Dijkstra's algorithm for shortest paths and Kruskal's algorithm for minimum spanning trees.
Developers should learn weighted graphs when working on applications involving optimization, pathfinding, or network analysis, such as GPS navigation systems, logistics planning, or social network analysis with interaction strengths. They are essential in computer science for solving problems in algorithms, data structures, and discrete mathematics, providing a foundation for efficient solutions in fields like machine learning, game development, and telecommunications.