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Expander graph

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer networks, and the theory of error-correcting codes.

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

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Applications and useful properties

Computer scienceAlgorithmsError correcting codesExtractorsPseudorandom generators
18 related topics

Definitions

MultigraphBoundaryConnected componentComplete graphDegree
23 related topics

Constructions

Additive combinatoricsZig-zagFinite geometriesAlgebraicCayley graphs
26 related topics

Relationships between different expansion properties

AlonMilmanHypercubeCheeger boundMarkov chains
7 related topics

Topics to explore

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Overview

Definitions

Relationships between different expansion properties

Constructions

Applications and useful properties

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

Expander graph

Nodes89
Edges88
Triples56
Avg. degree1.98
Density0.022472
Components1

How this topic connects Entity context

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Expander graph

Top relations

has application · 11
Expander graph → Ajtai, Dinur, Expander, In, Komlós, PCP, Reingold, SL, Szemerédi, The, They
related to Margulis–Gabber–Galil · 9
Expander graph → Algebraic, Cayley, For, Gabber, Galil, Gn, Margulis, The, Then
related to AKS sorting network and approximate halvers · 7
Expander graph → AKS, An, Expander, Sorting, The, While, Within
related to Expander walk sampling · 7
Expander graph → Ajtai, Gillman, Komlós, Szemerédi, The, The Chernoff, This
related to Notes · 6
Expander graph → Alexander, Clark, DM, Expander Graphs, Fixed Size, On Near Optimal Spectral
related to Zig-zag product · 6
Expander graph → If, Reingold, Roughly, Therefore, Vadhan, Wigderson
related to Definitions · 5
Expander graph → Different, Every, Informally, Intuitively, The
related to Constructions · 3
Expander graph → Noga Alon, The, There
is a · 2
Expander graph → finite, sparse graph that has strong connectivity properties

Important terminology Word statistics

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Important terminology

graph graphs expander vertices expansion edge vertex displaystyle d-regular number spectral edges two degree λ2 zig-zag eigenvalues alon also every

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Expander graphis asparse graph that has strong connectivity properties0.90text
Expander graphis afinite0.90text
Expander graphhas applicationThe0.60section
Expander graphhas applicationExpander0.60section
Expander graphhas applicationAjtai0.60section
Expander graphhas applicationKomlós0.60section
Expander graphhas applicationSzemerédi0.60section
Expander graphhas applicationThey0.60section
Expander graphhas applicationSL0.60section
Expander graphhas applicationReingold0.60section
Expander graphhas applicationPCP0.60section
Expander graphhas applicationDinur0.60section

Related concept clusters Concept neighborhoods

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    Connections between topic areas Semantic bridges

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    Min side: 3
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