Suggest an editImprove this articleRefine the answer for “What is a weighted graph?”. Your changes go to moderation before they’re published.Approval requiredContentWhat you’re changing🇺🇸EN🇺🇦UAPreviewTitle (EN)Short answer (EN)A **weighted graph** is a graph in which **every edge is assigned a weight (a numeric value)**. **Key point:** a weighted graph is a graph where every edge has a weight that reflects the "cost" of the connection between vertices.Shown above the full answer for quick recall.Answer (EN)ImageA **weighted graph** is a graph in which **every edge is assigned a weight (a numeric value)**. **Edge weight** is a characteristic of the connection between vertices: distance, cost, time, connection strength, and so on. --- ### Formally A weighted graph is **G = (V, E, w)**, where **w(u, v)** is a function that defines the **weight of edge (u, v)**. --- ### Example Let there be vertices - cities: **A**, **B**, **C**, and edges with distances: - **A-B (5 km)** - **B-C (3 km)** - **A-C (8 km)** Then the edge weights are 5, 3, and 8. --- ### Applications - Maps and navigation (weight = distance or time). - Cost optimization (weight = price). - Shortest-path algorithms (Dijkstra, Bellman-Ford). --- **Summary:** a weighted graph is a graph where every edge has a **weight** that reflects the "cost" of the connection between vertices.For the reviewerNote to the moderator (optional)Visible only to the moderator. Helps review go faster.