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Line graph

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).

Characters, Properties & Generalizations

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

Explore this topic

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Topics to explore

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Overview

Formal definition

Properties

Characterization and recognition

Iterating the line graph operator

Generalizations

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

Line graph

Nodes100
Edges99
Triples101
Avg. degree1.98
Density0.02
Components1

How this topic connects Entity context

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

Line graph

Top relations

related to Strongly regular and perfect line graphs · 18
Line graph → C3, C4, C5, Chang, It, Johnson, K4, K8, KGn, Kn, Kneser, Kőnig's, Like, Shrikhande, The, They, Triangular, When
related to Weighted line graphs · 11
Line graph → For, If, In, It, On, One, Put, The, There, This, Whitney
related to Algorithms · 9
Line graph → Degiorgi, However, It, Lehot, Roussopoulos, Simon, Sysło, The, Whitney's
related to Forbidden subgraphs · 9
Line graph → Another, Beineke, Beineke's, For, He, In, K1, That, Therefore
related to Multigraphs · 8
Line graph → For, However, In, K1, Nevertheless, Shannon, The, Whitney's
related to Whitney isomorphism theorem · 8
Line graph → As, For, However, If, In, K1, K3, Whitney
related to Clique partition · 7
Line graph → By, Each, For, Given, It, The, Whitney's
related to Medial graphs and convex polyhedra · 7
Line graph → An, However, It, K1, The, These, When
related to Example · 6
Line graph → Each, For, GAdded, Graph GVertices, Green, The
related to Line digraphs · 6
Line graph → Bruijn, If, It, That, The, Two

Important terminology Word statistics

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Important terminology

graph line graphs vertex vertices edges two edge one connected perfect theorem degree number adjacent case corresponding used set may

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the small-world propertyinstance ofthe line graph of a random network preserves many of the properties of the network0.80text
Line graphrelated to AlgorithmsRoussopoulos0.60section
Line graphrelated to AlgorithmsLehot0.60section
Line graphrelated to AlgorithmsSysło0.60section
Line graphrelated to AlgorithmsDegiorgi0.60section
Line graphrelated to AlgorithmsSimon0.60section
Line graphrelated to AlgorithmsThe0.60section
Line graphrelated to AlgorithmsHowever0.60section
Line graphrelated to AlgorithmsWhitney's0.60section
Line graphrelated to AlgorithmsIt0.60section
Line graphrelated to Clique partitionFor0.60section
Line graphrelated to Clique partitionThe0.60section

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

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    Min side: 3
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