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Graph theory: History, Applications, Science & Products

In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links, or lines). A distinction is made between undirected graphs, where…

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Graph theory topic overview

The analysis highlights History, Applications, Science and Products as prominent areas in the source structure around Graph theory. 2 topics appear in more than one source area, which can help identify connections that are less obvious in a linear reading.

Related topics
312
Source areas
8
Connected nodes
322
Extracted relationships
500
Concept neighborhoods
142
Bridge connections
322

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.

Subareas · 130 topics
History · 53 topics
Problems · 52 topics
Applications · 49 topics
Representation · 12 topics
Overview · 8 topics
Definition and etymology · 7 topics
Online textbooks · 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

Definition and etymology

History

Subareas

Applications

Representation

Problems

Online textbooks

  • ArXiv ArXiv (identifier)
  • Doi Doi (identifier)
  • ISBN ISBN (identifier)

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 Graph theory connects Entity context

The extracted context around Graph theory shows recurring relationship patterns in the source. For example, Graph theory → Academic Press, Achilleas, ACM, Addison-Wesley, Additive Combinatorics, Advances, Ahcene, AID-RSA10, Alan, Algebra, Algebraic Graph Theory, Algebraic Methods, Algorithmic Graph Theory, Algorithms, American Mathematical Society, AMS/MAA, An Introduction, Analysis, Analytischen Figuren, Andreev's Another extracted example is Graph theory → Alexandre-Théophile Vandermonde's, Arthur Cayley, Augustin-Louis Cauchy, Bruijn, Cayley, Enumerative, Euler's, Geometriam Situs Pertinentis, Gottfried Wilhelm Leibniz, In, Johann Benedict Listing, Königsberg, Leonhard Euler, More, Nicolaas Govert, Problèmes, Pólya, Remarques, Seven Bridges, Simon Antoine Jean L'Huilier. Use these groups to spot repeated connection types before inspecting the individual relationships.

Graph theory

Top relations

related to References · 360
Graph theory → Academic Press, Achilleas, ACM, Addison-Wesley, Additive Combinatorics, Advances, Ahcene, AID-RSA10, Alan, Algebra, Algebraic Graph Theory, Algebraic Methods, Algorithmic Graph Theory, Algorithms, American Mathematical Society, AMS/MAA, An Introduction, Analysis, Analytischen Figuren, Andreev's
related to history · 25
Graph theory → Alexandre-Théophile Vandermonde's, Arthur Cayley, Augustin-Louis Cauchy, Bruijn, Cayley, Enumerative, Euler's, Geometriam Situs Pertinentis, Gottfried Wilhelm Leibniz, In, Johann Benedict Listing, Königsberg, Leonhard Euler, More, Nicolaas Govert, Problèmes, Pólya, Remarques, Seven Bridges, Simon Antoine Jean L'Huilier
related to Online textbooks · 18
Graph theory → Alexander, Algorithms, Applications, Basics, Combinatorial Optimization Problems, Digraphs, Gregory GutinGraph Theory, Hartmann, Introduction, ISBN, Jorgen Bang-Jensen, Martin, Phase Transitions, Reinhard Diestel, Statistical Mechanics, Theory Algorithms, Weigt, Wiley
related to External links · 14
Graph theory → Archived, Concise, EMS Press, Encyclopedia, February, Graph, Graphs, IDEThe Social Life, Image, Mathematics, Routers, Theory Software, Wayback Machine, Wayback MachineA
related to Extremal graph theory · 10
Graph theory → Being, Erdős, Extremal, Mantel's, Stone, Szemerédi, Szemerédi's, The, This, Turán's
related to Graph coloring · 10
Graph theory → Among, Behzad's, Faber, Four-color, Hadwiger, List, Lovász, Many, One, Typically
related to Physics and chemistry · 9
Graph theory → Also, Chemical, Feynman, Graph, Graphs, In, Removal, Similarly, This
related to Definition and etymology · 8
Graph theory → Graph, It, James Joseph Sylvester, Nature, Occasionally, Such, The, Two
related to Topological graph theory · 7
Graph theory → Crossing, Embedding, Heawood, The, This, Topological, United States
related to Biology and ecology · 6
Graph theory → Another, Evolutionary, For, Graphs, Likewise, This

Important terminology

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

Important terminology

graph graphs theory vertices edges isbn problem also random planar number theorem structures two tree mathematics called doi structure used

Graph theory relationships Subject–Predicate–Object triples

TTTA extracted 500 structured relationships around Graph theory. Examples in this analysis include Graph theory → is a → study of graphs and Graph theory → is a → four color problem. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Graph theoryis astudy of graphs0.90text
Graph theoryis afour color problem0.90text
Graph theoryis astudy of graph theory that involves major branches of algebra0.90text
Graph theoryis abranch of mathematics at the intersection of extremal combinatorics and graph theory0.90text
head-driven phrase structure grammar model the syntax of natural language using typed feature structuresinstance ofMore contemporary approaches0.80text
which are directed acyclic graphsinstance ofMore contemporary approaches0.80text
TextGraphsinstance ofthe usefulness of this area of mathematics to linguistics has borne organizations0.80text
as well as various 'Net' projectsinstance ofthe usefulness of this area of mathematics to linguistics has borne organizations0.80text
such as WordNetinstance ofthe usefulness of this area of mathematics to linguistics has borne organizations0.80text
VerbNetinstance ofthe usefulness of this area of mathematics to linguistics has borne organizations0.80text
and others.Physicsinstance ofthe usefulness of this area of mathematics to linguistics has borne organizations0.80text
chemistryGraph theory is also used to study molecules in chemistryinstance ofthe usefulness of this area of mathematics to linguistics has borne organizations0.80text

Related concept clusters Concept neighborhoods

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

  • Graph theory
    • Theory
    • Edges
    • Vertices
    • Graphs
    • Number
    • Also
    • Planar
    • Theorem
    • Intersection
    • Applications
    • Problem
    • Called
  • graph theory
    • Theory
    • Edges
    • Vertices
    • Graphs
    • Also
    • Number
    • Planar
    • Theorem
    • Intersection
    • Applications
    • Problem
    • Called
  • graphs
    • Theory
    • Used
    • Problems
    • Represent
    • Two
    • Study
    • Many
    • Structures
    • Random
    • Also
    • Algorithms
    • Vertices
  • vertices
    • Edges
    • Connected
    • Two
    • Graph
    • Represent
    • One
    • Called
    • Matrix
    • Edge
    • Number
    • Also
    • Tree
  • edges
    • Vertices
    • Graph
    • Represent
    • Number
    • One
    • Known
    • Many
    • Used
    • Two
    • Graphs
    • Matrix
    • Coloring
  • directed graphs
    • Theory
    • Used
    • Problems
    • Represent
    • Two
    • Study
    • Many
    • Structures
    • Random
    • Also
    • Algorithms
    • Vertices
  • mixed graph
    • Theory
    • Edges
    • Vertices
    • Graphs
    • Number
    • Also
    • Planar
    • Theorem
    • Intersection
    • Problem
    • Called
    • One
  • enumeration of graphs
    • Theory
    • Used
    • Problems
    • Represent
    • Two
    • Study
    • Many
    • Structures
    • Random
    • Also
    • Algorithms
    • Vertices

Connections between topic areas Semantic bridges

For Graph theory, one of the stronger structural bridges in this analysis connects Graph theory with Subareas. 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
Graph theorySubareas · splits 192 ⟂ 131
Graph theoryHistory · splits 269 ⟂ 54
Graph theoryProblems · splits 270 ⟂ 53
Graph theoryApplications · splits 273 ⟂ 50
Graph theoryRepresentation · splits 310 ⟂ 13
Graph theoryOverview · splits 314 ⟂ 9
Graph theoryDefinition and etymology · splits 315 ⟂ 8
Graph theoryOnline textbooks · splits 319 ⟂ 4

Map overview Semantic statistics

Graph theory

Nodes323
Edges322
Triples500
Avg. degree1.99
Density0.006192
Components1

Source & methodology

TTTA analyzes the structure around Graph theory to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, Applications, Science & Products, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Graph theory · EN edition · Analysis: TopicsToTalkAbout

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