Research any topic before you write.

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

Cycle basis

In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every even-degree subgraph to be expressed as a symmetric difference of basis cycles.

Applications, Special cycle bases & Minimum weight

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 Cycle basis. 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

Definitions

Special cycle bases

Minimum weight

Applications

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

Cycle basis

Nodes72
Edges71
Triples60
Avg. degree1.97
Density0.027778
Components1

How this topic connects Entity context

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

Cycle basis

Top relations

related to Face cycles · 10
Cycle basis → As, By Euler's, Eulerian, For, If, In, It, Mac Lane's, One, The
related to Polynomial time algorithms · 10
Cycle basis → As Horton, Gaussian, His, Horton, However, In, Subsequent, Testing, There, Using Dijkstra's
related to In planar graphs · 6
Cycle basis → Based, Gomory, However, Hu, The, This
related to Minimum weight · 6
Cycle basis → By, Eulerian, For, If, The, Veblen's
related to Definitions · 5
Cycle basis → Eulerian, Every, It, The, This
related to Fundamental cycles · 5
Cycle basis → Each, If, It, There, Therefore
related to NP-hardness · 5
Cycle basis → Finding, Hamiltonian, If, MAXSNP-hard, NP-hard
related to Integral bases · 4
Cycle basis → An, Less, The, This
is a · 3
Cycle basis → basis of this vector space in which each basis vector represents a simple cycle, Horton cycle, set of simple cycles that generates this group
has application · 2
Cycle basis → Cycle, In

Important terminology Word statistics

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

Important terminology

cycle basis graph cycles weight fundamental minimum set displaystyle edge edges planar every given bases space may tree one eulerian

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cycle basisis abasis of this vector space in which each basis vector represents a simple cycle0.90text
Cycle basisis aset of simple cycles that generates this group0.90text
Cycle basisis aHorton cycle0.90text
Cycle basishas applicationCycle0.60section
Cycle basishas applicationIn0.60section
Cycle basisrelated to DefinitionsEulerian0.60section
Cycle basisrelated to DefinitionsEvery0.60section
Cycle basisrelated to DefinitionsThe0.60section
Cycle basisrelated to DefinitionsIt0.60section
Cycle basisrelated to DefinitionsThis0.60section
Cycle basisrelated to Face cyclesIf0.60section
Cycle basisrelated to Face cyclesOne0.60section

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.