Research any topic before you write.

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

Cyclomatic number: Applications, Formula & The number of independent cycles

In graph theory, a branch of mathematics, the cyclomatic number, circuit rank, cycle rank, corank or nullity of an undirected graph is the minimum number of edges that must be removed from the graph to break all its cycles, making it into a tree or forest.

Language: English [EN]
Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.
100%
More settings
100% 100% 100% 100% 100%

Cyclomatic number topic overview

The analysis highlights Applications, Formula and The number of independent cycles as prominent areas in the source structure around Cyclomatic number.

Related topics
57
Source areas
7
Connected nodes
64
Extracted relationships
38
Concept neighborhoods
37
Bridge connections
64

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.

Formula · 19 topics
Applications · 14 topics
Overview · 7 topics
The number of independent cycles · 7 topics
Related concepts · 4 topics
For hypergraphs · 3 topics
Matroid rank and construction of a minimum feedback edge set · 3 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.

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

Formula

For hypergraphs

Matroid rank and construction of a minimum feedback edge set

The number of independent cycles

Applications

Related concepts

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.

How Cyclomatic number connects Entity context

The extracted context around Cyclomatic number shows recurring relationship patterns in the source. For example, Cyclomatic number → Any, Because, Betti, In, Intuitively, More, The, This Another extracted example is Cyclomatic number → Another, Both, It, NP-hard, The, This. Use these groups to spot repeated connection types before inspecting the individual relationships.

Cyclomatic number

Top relations

related to The number of independent cycles · 8
Cyclomatic number → Any, Because, Betti, In, Intuitively, More, The, This
related to Generalizations to directed graphs · 6
Cyclomatic number → Another, Both, It, NP-hard, The, This
related to For hypergraphs · 4
Cyclomatic number → It, Levi, The, This
related to Ear decomposition · 3
Cyclomatic number → In, The, This
related to Formula · 3
Cyclomatic number → It, The, Unlike
related to Matroid rank and construction of a minimum feedback edge set · 3
Cyclomatic number → Alternatively, The, Using
related to Meshedness coefficient · 3
Cyclomatic number → For, Here, The
related to Parametrized complexity · 3
Cyclomatic number → An, NP-hard, Some
is a · 2
Cyclomatic number → minimum feedback arc set, rank of the first
related to Computational chemistry · 2
Cyclomatic number → Frèrejacque, In

Important terminology

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

Important terminology

number graph cyclomatic rank edges cycles set graphs cycle vertices minimum displaystyle directed forest theory feedback independent ear decomposition hypergraph

Cyclomatic number relationships Subject–Predicate–Object triples

TTTA extracted 38 structured relationships around Cyclomatic number. Examples in this analysis include Cyclomatic number → is a → rank of the first and Cyclomatic number → is a → minimum feedback arc set. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Cyclomatic numberis arank of the first0.90text
Cyclomatic numberis aminimum feedback arc set0.90text
Cyclomatic numberrelated to Almost-treesSeveral0.60section
Cyclomatic numberrelated to Computational chemistryIn0.60section
Cyclomatic numberrelated to Computational chemistryFrèrejacque0.60section
Cyclomatic numberrelated to Ear decompositionThe0.60section
Cyclomatic numberrelated to Ear decompositionIn0.60section
Cyclomatic numberrelated to Ear decompositionThis0.60section
Cyclomatic numberrelated to For hypergraphsThe0.60section
Cyclomatic numberrelated to For hypergraphsLevi0.60section
Cyclomatic numberrelated to For hypergraphsIt0.60section
Cyclomatic numberrelated to For hypergraphsThis0.60section

Related concept clusters Concept neighborhoods

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

  • Cyclomatic number
    • Number
    • Graph
    • Edges
    • Graphs
    • Displaystyle
    • Rank
    • Set
    • Called
    • Formula
    • Cycles
    • Theory
    • Cycle
  • cyclomatic number
    • Number
    • Graph
    • Graphs
    • Edges
    • Displaystyle
    • Set
    • Vertices
    • Rank
    • Called
    • Formula
    • Cycles
    • Theory
  • graph theory
    • Number
    • Cyclomatic
    • Matroid
    • Displaystyle
    • Edges
    • Rank
    • Space
    • Also
    • Using
    • Cycle
    • Graphs
    • Set
  • undirected graph
    • Number
    • Circuit
    • Cyclomatic
    • Displaystyle
    • Edges
    • Rank
    • Cycle
    • Graphs
    • Set
    • Cycles
    • Decomposition
    • Ear
  • cycles
    • Minimum
    • Breaks
    • Independent
    • Edges
    • Set
    • Forest
    • Using
    • Number
    • Directed
    • Graph
    • Cyclomatic
    • Rank
  • cycle basis
    • Rank
    • Minimum
    • Theory
    • Cycles
    • Graph
    • Matroid
    • Tree
    • Set
    • Edge
    • Space
    • Vertex
    • Feedback
  • feedback arc set
    • Arc
    • Feedback
    • Directed
    • Minimum
    • Set
    • Breaks
    • Graphs
    • Edge
    • Formula
    • Using
    • Vertices
    • Edges
  • directed graphs
    • Graphs
    • Feedback
    • Arc
    • Set
    • Minimum
    • Number
    • Meshedness
    • Edges
    • Edge
    • Formula
    • Rank
    • Graph

Connections between topic areas Semantic bridges

For Cyclomatic number, one of the stronger structural bridges in this analysis connects Cyclomatic number with Formula. 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
Cyclomatic number — Formula · splits 45 ⟂ 20
Cyclomatic number — Applications · splits 50 ⟂ 15
Cyclomatic number — Overview · splits 57 ⟂ 8
Cyclomatic number — The number of independent cycles · splits 57 ⟂ 8
Cyclomatic number — Related concepts · splits 60 ⟂ 5
Cyclomatic number — For hypergraphs · splits 61 ⟂ 4
Cyclomatic number — Matroid rank and construction of a minimum feedback edge set · splits 61 ⟂ 4

Map overview Semantic statistics

Cyclomatic number

Nodes65
Edges64
Triples38
Avg. degree1.97
Density0.030769
Components1

Source & methodology

TTTA analyzes the structure around Cyclomatic number to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Applications, Formula & The number of independent cycles, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Cyclomatic number · EN edition · Analysis: TopicsToTalkAbout

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