Research any topic before you write.

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

Matroid

In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the…

History & Research

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 Matroid. 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

Definition

Examples

Basic constructions

Additional terms

Algorithms

Matroid software

Polynomial invariants

Infinite matroids

History

Researchers

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

Matroid

Nodes144
Edges143
Triples111
Avg. degree1.99
Density0.013889
Components1

How this topic connects Entity context

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

Matroid

Top relations

related to External links · 10
Matroid → Brooklyn, Brooklyn College, City University, EMS Press, Encyclopedia, Kingan, Mathematics, New York, NY, Sandra
related to Matroid software · 9
Matroid → Both, Hlineny's Macek, Kingan's Oid, Macaulay2, Macek, Maple, Oid, SAGE, Two
related to history · 8
Matroid → Because, His, In, It, Kuroda, Nishimura, Takeo Nakasawa, Whitney
related to Uniform matroids · 8
Matroid → Additional, All, An, In, Let, One, The, This
see also · 8
Matroid → Abstraction, Antimatroid, Formulation, Generalization, Group-theoretic, Mathematical, Multiset, Set
is a · 7
Matroid → bicircular matroid of G, matroid in which every proper, matroid that is representable over all possible fields, simplest example of a matroid that is not representable over any field, simplest example of a matroid that is not representable over any field.Matroids from graph theoryA second original source for the theory of matroids is graph theory.Every finite…, size of its smallest circuit or dependent set.An element that forms a single-element circuit of M is called a loop, strict gammoid and vice versa.ExampleThe cycle matroid of a graph is the dual matroid of its bond matroid
related to Minors · 5
Matroid → Equivalently, If, In, Its, The
related to Rank functions · 5
Matroid → If, It, R1, The, This
related to Algorithms · 4
Matroid → Finding, In, Several, This
related to Duality · 4
Matroid → For, If, It, The

Important terminology Word statistics

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

Important terminology

displaystyle set matroids called rank independent theory sets subset subsets finite every graph elements element field one polynomial linear equivalent

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Matroidis amatroid in which every proper0.90text
Matroidis amatroid that is representable over all possible fields0.90text
Matroidis asimplest example of a matroid that is not representable over any field.Matroids from graph theoryA second original source for the theory of matroids is graph theory.Every finite…0.90text
Matroidis abicircular matroid of G0.90text
Matroidis asimplest example of a matroid that is not representable over any field0.90text
Matroidis astrict gammoid and vice versa.ExampleThe cycle matroid of a graph is the dual matroid of its bond matroid0.90text
Matroidis asize of its smallest circuit or dependent set.An element that forms a single-element circuit of M is called a loop0.90text
Matroidrelated to Additional termsLet0.60section
Matroidrelated to Additional termsIts0.60section
Matroidrelated to AlgorithmsSeveral0.60section
Matroidrelated to AlgorithmsIn0.60section
Matroidrelated to AlgorithmsFinding0.60section

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.