Weighted graph

Q: How deeply does Optimization Algorithms: AI techniques for design, planning, and control problems cover weighted graph?

Defines edge weights and demonstrates NetworkX construction, then connects them to shortest-path search without deriving algorithm internals.

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A graph whose edges have numerical weights representing quantities such as distance or cost.

A weighted graph assigns a numerical value to each edge. The value can represent distance, travel time, traversal cost, connection speed, or another application-specific metric. In a road network, edges may measure distance or time; in a telecommunications network, they may represent usage cost or connection speed. section 3.1

Weights turn graph connectivity into a basis for comparing routes. Dijkstra’s algorithm solves the single-source shortest-path problem when edge costs are non-negative, while uniform-cost search selects a path by its lowest cumulative cost. section 3.6

Telecommunication devices

A small network can connect Device1, Device2, Device3, and Device4 with weighted edges such as 45.69, 56.34, and 18.5. These values represent connection speeds in Mbps and can be displayed beside the edges. section 3.1

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

Cover of Optimization Algorithms: AI techniques for design, planning, and control problems

liveBook manning.com

Read Optimization Algorithms: AI techniques for design, planning, and control problems on liveBook Get the book at manning.com

Also explained in

liveBook manning.com

Classic Computer Science Problems in Swift: Essential techniques for practicing programmersA weighted graph is a graph whose edges have associated values representing connection costs or other quantities.
liveBook manning.com

Graph Algorithms for Data ScienceA weighted network is a graph whose relationships carry numerical values representing strength, cost, frequency, or another quantity.

Compare how 3 books explain 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 value that represents or determines the relative contribution, influence, importance, strength, likelihood, or resource amount of an element in a calculation, model, or system.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.