Weighted graph
A weighted graph is a graph whose edges have associated values representing quantities such as cost, distance, strength, or frequency.
Classic Computer Science Problems in Swift: Essential techniques for practicing programmers
A weighted graph is a graph whose edges have associated values representing connection costs or other quantities.
- How it is used
- Represents connection distances for minimum-cost network construction and shortest routes between cities.
- How deep it goes
- Builds generic weighted edges and adjacency lists, then walks through priority-queue implementations of spanning-tree and shortest-path searches.
- Examples
- Uses mile-weighted links among 15 U.S. metropolitan areas, a 5372-mile spanning tree, and a 2605-mile Los Angeles–Boston route.
- What you can do after
- Build it from scratch as a generic Swift graph and apply it to minimum spanning trees and single-source shortest paths.
Optimization Algorithms: AI techniques for design, planning, and control problems
A graph whose edges have numerical weights representing quantities such as distance or cost.
- How it is used
- Models distances, costs, times, or connection speeds so graph routes and relationships can be compared quantitatively.
- How deep it goes
- Defines edge weights and demonstrates NetworkX construction, then connects them to shortest-path search without deriving algorithm internals.
- Examples
- Uses road networks with distance or cost and telecommunications devices whose edges carry Mbps connection speeds.
- What you can do after
- Operate/configure weighted graphs with NetworkX and visualize nodes, edges, and numerical labels.
Graph Algorithms for Data Science
A weighted network is a graph whose relationships carry numerical values representing strength, cost, frequency, or another quantity.
- How it is used
- Represents relationship strength or traversal cost in network models.
- How deep it goes
- Defines numerical relationship weights and explains when higher or lower values are preferred.
- Examples
- Uses friendship relationships, transportation networks, and projected retweet networks as examples of weighted analysis.
- What you can do after
- Evaluate whether relationship values should be maximized for strength or minimized for traversal cost.
Read how Graph Algorithms for Data Science explains weighted graph →
Related concepts
- graphkind of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
- unweighted graphcontrasts with · An unweighted graph is a graph whose edges have no assigned numerical weights.
- Dijkstra's algorithmused by · Dijkstra's algorithm computes shortest paths from a source vertex in a weighted graph with nonnegative edge weights.
- UMAPused by · UMAP, or Uniform Manifold Approximation and Projection, is a nonlinear manifold-learning technique that embeds high-dimensional data in a lower-dimensional space while preserving important neighborhood and structural relationships.
- weighthas part · A weight is a numerical quantity assigned to an element to represent its contribution, influence, importance, strength, or resource amount in a calculation or system.
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