Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Transitive reduction

In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges as possible, such that for all pairs v, w of vertices, a (directed) path from v to w in D exists if and only if such a path exists in the reduction. Transitive reductions were introduced by Aho, Garey &…

Computational complexity, Classes of graphs & Overview

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Transitive reduction. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Classes of graphs

Computational complexity

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Transitive reduction

Nodes49
Edges48
Triples103
Avg. degree1.96
Density0.040816
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Transitive reduction

Top relations

related to References · 58
Transitive reduction → ACM, Aho, Alla, An, An Algorithm, Application, Becvár, Clough, Complex Networks, Computer Science, Computing, Czechoslovakia, Dennis, Digraph, Doklady Akademii Nauk SSSR, Evans, Finding, Furman, Garey, Gerald
related to Computing the reduction using the closure · 7
Transitive reduction → AB, Aho, Boolean, In, Then, They, To
related to In directed acyclic graphs · 7
Transitive reduction → For, If, In, Specifically, That, The, Transitivity
related to In infinite graphs · 7
Transitive reduction → Aho, Choosing, Form, However, It, Then, Therefore
related to Output-sensitive · 5
Transitive reduction → For, Initialize, Output, Replace, The
related to Computational complexity · 4
Transitive reduction → As Aho, Boolean, It, The
related to Computing the closure using the reduction · 4
Transitive reduction → Aho, In, Therefore, To
related to Computing the reduction in sparse graphs · 4
Transitive reduction → From, This, To, When
related to In graphs with cycles · 4
Transitive reduction → Additionally, If, In, Nevertheless
related to External links · 3
Transitive reduction → Eric, MathWorld, Weisstein

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

transitive reduction graph directed graphs edges acyclic vertices closure edge given relation vertex minimum subgraph path set reachability time possible

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Transitive reductionrelated to Computational complexityAs Aho0.60section
Transitive reductionrelated to Computational complexityIt0.60section
Transitive reductionrelated to Computational complexityBoolean0.60section
Transitive reductionrelated to Computational complexityThe0.60section
Transitive reductionrelated to Computing the closure using the reductionTo0.60section
Transitive reductionrelated to Computing the closure using the reductionAho0.60section
Transitive reductionrelated to Computing the closure using the reductionIn0.60section
Transitive reductionrelated to Computing the closure using the reductionTherefore0.60section
Transitive reductionrelated to Computing the reduction in sparse graphsWhen0.60section
Transitive reductionrelated to Computing the reduction in sparse graphsTo0.60section
Transitive reductionrelated to Computing the reduction in sparse graphsFrom0.60section
Transitive reductionrelated to Computing the reduction in sparse graphsThis0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.