Weighted Graph

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Figure:

A weighted graph assigns a numerical cost or distance to each edge. These weights are essential for algorithms like Dijkstra, Prim, and Kruskal, which optimize paths or networks.

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data_structure graph abstract_data_type nonlinear edge_weighted edge_labeled discrete_structure

Related Topic(s):

🔥 Minimum Spanning Tree → Minimum spanning tree is defined on an undirected weighted graph; MST algorithms rely on edge weights to compare and minimize total cost.

🔥 Shortest Path → Shortest-path algorithms on weighted graphs minimize total path cost by aggregating edge weights (typically summing) and performing edge relaxations; weight properties (e.g., non-negative vs. negative) determine algorithm choice (Dijkstra vs. Bellman–Ford) and correctness.

🔥 Graph Cost → Graph cost metrics (e.g., path cost, MST total weight, cut cost) depend on aggregating edge weights; without a weighted graph, these cost definitions are undefined or degenerate.

🌟 Kruskal Algorithm →

🌟 Dijkstra Algorithm →

🌟 Prim Algorithm →

🌟 Markov Chain →

Floyd-Warshall Algorithm →

Boruvka Algorithm →

Maximum Spanning Tree →

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