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Cycle basis: Applications, Special cycle bases & Minimum weight

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.

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Cycle basis topic overview

The analysis highlights Applications, Special cycle bases and Minimum weight as prominent areas in the source structure around Cycle basis.

Related topics
66
Source areas
5
Connected nodes
71
Extracted relationships
29
Related term clusters
31
Bridge connections
71

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Special cycle bases · 20 topics
Minimum weight · 14 topics
Overview · 13 topics
Applications · 11 topics
Definitions · 8 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definitions

Special cycle bases

Minimum weight

Applications

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Cycle basis connects Entity context

The extracted context around Cycle basis shows recurring relationship patterns in the source. For example, Cycle basis → As Horton, Gaussian, Horton, Subsequent, Testing, Using Dijkstra's Another extracted example is Cycle basis → By Euler's, Eulerian, Mac Lane's, One. Use these groups to spot repeated connection types before inspecting the individual relationships.

Cycle basis

Top relations

related to Polynomial time algorithms · 6
Cycle basis → As Horton, Gaussian, Horton, Subsequent, Testing, Using Dijkstra's
related to Face cycles · 4
Cycle basis → By Euler's, Eulerian, Mac Lane's, One
related to NP-hardness · 4
Cycle basis → Finding, Hamiltonian, MAXSNP-hard, NP-hard
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
related to In planar graphs · 3
Cycle basis → Based, Gomory, Hu
related to Definitions · 2
Cycle basis → Eulerian, Every
related to Minimum weight · 2
Cycle basis → Eulerian, Veblen's
has application · 1
Cycle basis → Cycle
related to Fundamental cycles · 1
Cycle basis → Therefore
related to Induced cycles · 1
Cycle basis → Every

Important terminology

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

Cycle basis relationships Subject–Predicate–Object triples

TTTA extracted 29 structured relationships around Cycle basis. Examples in this analysis include Cycle basis → is a → basis of this vector space in which each basis vector represents a simple cycle and Cycle basis → is a → set of simple cycles that generates this group. The table shows each extracted connection, where it came from and its confidence.

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 basisrelated to DefinitionsEulerian0.60section
Cycle basisrelated to DefinitionsEvery0.60section
Cycle basisrelated to Face cyclesOne0.60section
Cycle basisrelated to Face cyclesBy Euler's0.60section
Cycle basisrelated to Face cyclesEulerian0.60section
Cycle basisrelated to Face cyclesMac Lane's0.60section
Cycle basisrelated to Fundamental cyclesTherefore0.60section
Cycle basisrelated to In planar graphsGomory0.60section

Related concept clusters Related term clusters

The concept neighborhoods around Cycle basis bring nearby vocabulary together. In this analysis, examples include Basis, Cycle and Graph. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Cycle basis
    • Basis
    • Cycle
    • Graph
    • Cycles
    • Fundamental
    • Weight
    • Minimum
    • Bases
    • Edge
    • Planar
    • Every
    • Used
  • cycle basis
    • Basis
    • Cycle
    • Graph
    • Weight
    • Cycles
    • Minimum
    • Fundamental
    • Bases
    • Every
    • Set
    • Edge
    • Planar
  • graph theory
    • Edges
    • Planar
    • Given
    • Weight
    • Cycles
    • Minimum
    • May
    • Displaystyle
    • Set
    • Edge
    • Fundamental
    • Formed
  • undirected graph
    • Edges
    • Planar
    • Given
    • Weight
    • Cycles
    • Minimum
    • May
    • Displaystyle
    • Set
    • Edge
    • Fundamental
    • Formed
  • simple cycles
    • Set
    • Space
    • Graph
    • Fundamental
    • One
    • Minimum
    • Eulerian
    • Subgraph
    • Weight
    • Planar
    • Every
    • Given
  • basis
    • Cycle
    • Weight
    • Cycles
    • Minimum
    • Graph
    • Fundamental
    • Every
    • Set
    • Planar
    • Space
    • Time
    • Weakly
  • cycle space
    • Basis
    • Graph
    • Cycles
    • Fundamental
    • Weight
    • Minimum
    • Bases
    • Edge
    • Planar
    • Every
    • Used
    • Weakly
  • planar graph
    • Bounded
    • Edges
    • Embedding
    • Planar
    • Given
    • Weight
    • Cycles
    • Faces
    • Minimum
    • Set
    • May
    • Displaystyle

Connections between topic areas Semantic bridges

For Cycle basis, one of the stronger structural bridges in this analysis connects Cycle basis with Special cycle bases. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Cycle basis — Special cycle bases · splits 51 ⟂ 21
Cycle basis — Minimum weight · splits 57 ⟂ 15
Cycle basis — Overview · splits 58 ⟂ 14
Cycle basis — Applications · splits 60 ⟂ 12
Cycle basis — Definitions · splits 63 ⟂ 9

Map overview Semantic statistics

Cycle basis

Nodes72
Edges71
Triples29
Avg. degree1.97
Density0.027778
Components1

Source & methodology

TTTA analyzes the structure around Cycle basis to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Applications, Special cycle bases & Minimum weight, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Cycle basis · EN edition · Analysis: TopicsToTalkAbout

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