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Graph theory
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Mathematics
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482
Table of contents
482
1. Extensions and generalizations of graphs
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Graph theory
40
1.1. Directed graphs
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Extensions and generalizations of graphs
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1.1.1. Causal diagrams
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Directed graphs
1.1.2. Directed acyclic graphs
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Directed graphs
1.1.3. Aczel's anti-foundation axiom
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Directed graphs
1.1.4. Dependency graph
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Directed graphs
1.1.5. Dicut
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Directed graphs
1.1.6. Dijoin
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Directed graphs
1.1.7. Directed acyclic graph
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Directed graphs
1.1.8. Kautz graph
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Directed graphs
1.1.9. Lucchesi–Younger theorem
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Directed graphs
1.1.10. New digraph reconstruction conjecture
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Directed graphs
1.1.11. Random surfing model
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Directed graphs
1.1.12. St-connectivity
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Directed graphs
1.1.13. Strongly connected component
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Directed graphs
1.1.14. Table of vertex-symmetric digraphs
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Directed graphs
1.1.15. Tournament (graph theory)
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Directed graphs
1.1.16. Transpose graph
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Directed graphs
1.1.17. Wait-for graph
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Directed graphs
1.1.18. Why–because analysis
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Directed graphs
1.1.19. Woodall's conjecture
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Directed graphs
1.2. Hypergraphs
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Extensions and generalizations of graphs
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1.2.1. BF-graph
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Hypergraphs
1.2.2. Balanced hypergraph
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Hypergraphs
1.2.3. Bipartite hypergraph
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Hypergraphs
1.2.4. Container method
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Hypergraphs
1.2.5. D-interval hypergraph
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Hypergraphs
1.2.6. Hedgehog (hypergraph)
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Hypergraphs
1.2.7. Hypertree
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Hypergraphs
1.2.8. Line graph of a hypergraph
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Hypergraphs
1.2.9. Packing in a hypergraph
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Hypergraphs
1.2.10. Width of a hypergraph
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Hypergraphs
1.3. Ancestral graph
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Extensions and generalizations of graphs
1.4. Bidirected graph
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Extensions and generalizations of graphs
1.5. Graph labeling
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Extensions and generalizations of graphs
1.6. Multigraph
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Extensions and generalizations of graphs
1.7. Ordered graph
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Extensions and generalizations of graphs
1.8. Quantum graph
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Extensions and generalizations of graphs
1.9. Rooted graph
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Extensions and generalizations of graphs
1.10. Rotation map
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Extensions and generalizations of graphs
1.11. Voltage graph
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Extensions and generalizations of graphs
2. Extremal graph theory
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Graph theory
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2.1. Biclique-free graph
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Extremal graph theory
2.2. Common graph
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Extremal graph theory
2.3. Dependent random choice
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Extremal graph theory
2.4. Forbidden subgraph problem
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Extremal graph theory
2.5. Homomorphism density
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Extremal graph theory
2.6. Turán graph
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Extremal graph theory
2.7. Turán number
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Extremal graph theory
2.8. Zarankiewicz problem
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Extremal graph theory
3. Graph connectivity
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Graph theory
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3.1. Biconnected component
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Graph connectivity
3.2. Biconnected graph
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Graph connectivity
3.3. Bridge (graph theory)
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Graph connectivity
3.4. Component (graph theory)
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Graph connectivity
3.5. Connectivity (graph theory)
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Graph connectivity
3.6. Cut (graph theory)
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Graph connectivity
3.7. Cycle rank
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Graph connectivity
3.8. Giant component
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Graph connectivity
3.9. Graph toughness
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Graph connectivity
3.10. K-edge-connected graph
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Graph connectivity
3.11. K-vertex-connected graph
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Graph connectivity
3.12. Path (graph theory)
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Graph connectivity
3.13. Reachability
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Graph connectivity
3.14. SPQR tree
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Graph connectivity
3.15. Strength of a graph
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Graph connectivity
3.16. Strong orientation
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Graph connectivity
3.17. Vertex separator
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Graph connectivity
3.18. Weak component
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Graph connectivity
4. Graph databases
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Graph theory
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4.1. Resource Description Framework
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Graph databases
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4.1.1. RDF data access
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Resource Description Framework
4.1.2. RSS
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Resource Description Framework
4.1.3. Triplestores
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Resource Description Framework
4.1.4. Apache Jena
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Resource Description Framework
4.1.5. Data Catalog Vocabulary
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Resource Description Framework
4.1.6. Graph Style Sheets
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Resource Description Framework
4.1.7. JSON-LD
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Resource Description Framework
4.1.8. Linked Data Platform
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Resource Description Framework
4.1.9. List of SPARQL implementations
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Resource Description Framework
4.1.10. Metaclass (Semantic Web)
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Resource Description Framework
4.1.11. Notation3
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Resource Description Framework
4.1.12. RDF/XML
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Resource Description Framework
4.1.13. RDF4J
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Resource Description Framework
4.1.14. RDFLib
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Resource Description Framework
4.1.15. RDF Schema
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Resource Description Framework
4.1.16. RDF query language
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Resource Description Framework
4.1.17. RDFa
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Resource Description Framework
4.1.18. Redland RDF Application Framework
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Resource Description Framework
4.1.19. SHACL
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Resource Description Framework
4.1.20. SPARQL
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Resource Description Framework
4.1.21. Semantic triple
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Resource Description Framework
4.1.22. ShEx
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Resource Description Framework
4.1.23. Thing Description
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Resource Description Framework
4.1.24. TriG (syntax)
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Resource Description Framework
4.1.25. TriX (serialization format)
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Resource Description Framework
4.1.26. Turtle (syntax)
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Resource Description Framework
4.1.27. Web Ontology Language
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Resource Description Framework
4.1.28. XHTML+RDFa
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Resource Description Framework
4.2. AllegroGraph
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Graph databases
4.3. Amazon Neptune
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Graph databases
4.4. ArangoDB
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Graph databases
4.5. Blazegraph
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Graph databases
4.6. DataStax
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Graph databases
4.7. FlockDB
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Graph databases
4.8. Graph database
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Graph databases
4.9. InfiniteGraph
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Graph databases
4.10. JanusGraph
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Graph databases
4.11. Linkurious
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Graph databases
4.12. Mulgara (software)
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Graph databases
4.13. NebulaGraph
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Graph databases
4.14. Neo4j
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Graph databases
4.15. NitrosBase
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Graph databases
4.16. Ontotext GraphDB
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Graph databases
4.17. Oracle Spatial and Graph
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Graph databases
4.18. OrientDB
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Graph databases
4.19. Sones GraphDB
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Graph databases
4.20. Sparksee (graph database)
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Graph databases
4.21. TerminusDB
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Graph databases
4.22. TigerGraph
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Graph databases
4.23. TypeDB
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Graph databases
4.24. Vadalog
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Graph databases
5. Graph description languages
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Graph theory
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5.1. DGML
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Graph description languages
5.2. DOT (graph description language)
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Graph description languages
5.3. GXL
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Graph description languages
5.4. GraphML
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Graph description languages
5.5. Graph Modelling Language
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Graph description languages
5.6. LCF notation
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Graph description languages
5.7. Newick format
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Graph description languages
5.8. PGF/TikZ
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Graph description languages
5.9. Trivial Graph Format
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Graph description languages
5.10. XGMML
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Graph description languages
6. Graph invariants
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Graph theory
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6.1. (a, b)-decomposition
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Graph invariants
6.2. Bipartite dimension
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Graph invariants
6.3. Bondage number
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Graph invariants
6.4. Carving width
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Graph invariants
6.5. Cheeger constant (graph theory)
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Graph invariants
6.6. Clique-width
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Graph invariants
6.7. Closeness centrality
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Graph invariants
6.8. Colin de Verdière graph invariant
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Graph invariants
6.9. Cutwidth
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Graph invariants
6.10. Dissociation number
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Graph invariants
6.11. Entanglement (graph measure)
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Graph invariants
6.12. Friendly-index set
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Graph invariants
6.13. Girth (graph theory)
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Graph invariants
6.14. Graph pebbling
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Graph invariants
6.15. Hadwiger number
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Graph invariants
6.16. Hyper-Wiener index
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Graph invariants
6.17. Intersection number (graph theory)
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Graph invariants
6.18. Linear arboricity
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Graph invariants
6.19. Meshedness coefficient
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Graph invariants
6.20. Metric dimension (graph theory)
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Graph invariants
6.21. Pathwidth
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Graph invariants
6.22. Periodic graph (graph theory)
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Graph invariants
6.23. Sparsity matroid
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Graph invariants
6.24. Splittance
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Graph invariants
6.25. Strahler number
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Graph invariants
6.26. Tardos function
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Graph invariants
6.27. Thickness (graph theory)
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Graph invariants
6.28. Treewidth
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Graph invariants
6.29. Tutte–Grothendieck invariant
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Graph invariants
6.30. Twin-width
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Graph invariants
6.31. Vizing's conjecture
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Graph invariants
7. Graph minor theory
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Graph theory
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7.1. Apex graph
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Graph minor theory
7.2. Bounded expansion
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Graph minor theory
7.3. Bramble (graph theory)
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Graph minor theory
7.4. Clique-sum
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Graph minor theory
7.5. Graph minor
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Graph minor theory
7.6. Halin's grid theorem
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Graph minor theory
7.7. K-tree
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Graph minor theory
7.8. Kelmans–Seymour conjecture
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Graph minor theory
7.9. Partial k-tree
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Graph minor theory
7.10. Petersen family
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Graph minor theory
7.11. Planar cover
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Graph minor theory
7.12. Shallow minor
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Graph minor theory
7.13. Tree decomposition
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Graph minor theory
8. Graph operations
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Graph theory
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8.1. Graph products
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Graph operations
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8.1.1. Cartesian product of graphs
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Graph products
8.1.2. Graph product
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Graph products
8.1.3. Lexicographic product of graphs
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Graph products
8.1.4. Min-plus matrix multiplication
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Graph products
8.1.5. Modular product of graphs
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Graph products
8.1.6. Rooted product of graphs
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Graph products
8.1.7. Strong product of graphs
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Graph products
8.1.8. Tensor product of graphs
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Graph products
8.1.9. Zig-zag product
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Graph products
8.2. Bipartite double cover
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Graph operations
8.3. Bipartite half
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Graph operations
8.4. Clique graph
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Graph operations
8.5. Cograph
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Graph operations
8.6. Complement graph
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Graph operations
8.7. Disjoint union of graphs
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Graph operations
8.8. Edge contraction
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Graph operations
8.9. Goldberg–Coxeter construction
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Graph operations
8.10. Graph power
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Graph operations
8.11. Induced subgraph
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Graph operations
8.12. Line graph
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Graph operations
8.13. Medial graph
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Graph operations
8.14. Moral graph
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Graph operations
8.15. Mycielskian
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Graph operations
8.16. Quotient graph
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Graph operations
8.17. Series–parallel graph
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Graph operations
8.18. Simplex graph
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Graph operations
8.19. Y-Δ transform
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Graph operations
9. Graph theory objects
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Graph theory
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9.1. Hamiltonian paths and cycles
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Graph theory objects
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9.1.1. Barnette's conjecture
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Hamiltonian paths and cycles
9.1.2. Hamiltonian completion
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Hamiltonian paths and cycles
9.1.3. Herschel graph
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Hamiltonian paths and cycles
9.1.4. Hypohamiltonian graph
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Hamiltonian paths and cycles
9.1.5. Pancyclic graph
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Hamiltonian paths and cycles
9.1.6. Shortness exponent
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Hamiltonian paths and cycles
9.1.7. Subhamiltonian graph
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Hamiltonian paths and cycles
9.1.8. Tait's conjecture
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Hamiltonian paths and cycles
9.1.9. Walther graph
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Hamiltonian paths and cycles
9.2. Acyclic orientation
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Graph theory objects
9.3. Bipolar orientation
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Graph theory objects
9.4. Blossom tree (graph theory)
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Graph theory objects
9.5. Chordal completion
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Graph theory objects
9.6. Clique (graph theory)
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Graph theory objects
9.7. Core (graph theory)
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Graph theory objects
9.8. Cycle (graph theory)
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Graph theory objects
9.9. Edge-graceful labeling
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Graph theory objects
9.10. Edge cycle cover
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Graph theory objects
9.11. End (graph theory)
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Graph theory objects
9.12. Eternal dominating set
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Graph theory objects
9.13. Eulerian path
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Graph theory objects
9.14. Graceful labeling
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Graph theory objects
9.15. Graph center
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Graph theory objects
9.16. Hamiltonian decomposition
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Graph theory objects
9.17. Incidence (graph)
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Graph theory objects
9.18. Induced path
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Graph theory objects
9.19. Level structure
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Graph theory objects
9.20. Map (graph theory)
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Graph theory objects
9.21. Minimum cut
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Graph theory objects
9.22. Modular decomposition
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Graph theory objects
9.23. Multiple edges
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Graph theory objects
9.24. Neighbourhood (graph theory)
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Graph theory objects
9.25. Orientation (graph theory)
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Graph theory objects
9.26. Path cover
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Graph theory objects
9.27. Peripheral cycle
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Graph theory objects
9.28. Sachs subgraph
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Graph theory objects
9.29. Skew partition
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Graph theory objects
9.30. Split (graph theory)
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Graph theory objects
9.31. Unfriendly partition
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Graph theory objects
9.32. Universal vertex
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Graph theory objects
10. Graphs
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Graph theory
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10.1. Application-specific graphs
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Graphs
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10.1.1. Graph data structures
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Application-specific graphs
10.1.2. Trees (data structures)
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Application-specific graphs
10.1.3. Bratteli diagram
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Application-specific graphs
10.1.4. Bratteli–Vershik diagram
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Application-specific graphs
10.1.5. Citation graph
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Application-specific graphs
10.1.6. Co-stardom network
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Application-specific graphs
10.1.7. Code property graph
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Application-specific graphs
10.1.8. Collaboration graph
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Application-specific graphs
10.1.9. Conceptual graph
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Application-specific graphs
10.1.10. Configuration graph
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Application-specific graphs
10.1.11. Constraint graph
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Application-specific graphs
10.1.12. Constraint graph (layout)
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Application-specific graphs
10.1.13. Control-flow graph
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Application-specific graphs
10.1.14. Disjunctive graph
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Application-specific graphs
10.1.15. Eodermdrome
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Application-specific graphs
10.1.16. Evolutionary graph theory
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Application-specific graphs
10.1.17. Factor graph
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Application-specific graphs
10.1.18. Graph-structured stack
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Application-specific graphs
10.1.19. Ingredient-flavor network
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Application-specific graphs
10.1.20. Loss network
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Application-specific graphs
10.1.21. Prime graph
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Application-specific graphs
10.1.22. Process graph
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Application-specific graphs
10.1.23. Program dependence graph
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Application-specific graphs
10.1.24. Reeb graph
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Application-specific graphs
10.1.25. Tanner graph
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Application-specific graphs
10.1.26. Trellis (graph)
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Application-specific graphs
10.1.27. Webgraph
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Application-specific graphs
10.2. Graph families
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Graphs
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10.2.1. Intersection classes of graphs
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Graph families
10.2.2. Parametric families of graphs
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Graph families
10.2.3. Trees (graph theory)
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Graph families
10.2.4. Asymmetric graph
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Graph families
10.2.5. Bipartite graph
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Graph families
10.2.6. Bivariegated graph
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Graph families
10.2.7. Block graph
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Graph families
10.2.8. Bound graph
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Graph families
10.2.9. Cactus graph
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Graph families
10.2.10. Chordal bipartite graph
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Graph families
10.2.11. Chordal graph
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Graph families
10.2.12. Cluster graph
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Graph families
10.2.13. Comparability graph
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Graph families
10.2.14. Convex bipartite graph
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Graph families
10.2.15. Dense graph
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Graph families
10.2.16. Distance-hereditary graph
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Graph families
10.2.17. Dually chordal graph
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Graph families
10.2.18. Even-hole-free graph
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Graph families
10.2.19. Expander graph
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Graph families
10.2.20. Forcing graph
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Graph families
10.2.21. Geodetic graph
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Graph families
10.2.22. Halin graph
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Graph families
10.2.23. Hanan grid
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Graph families
10.2.24. Highly irregular graph
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Graph families
10.2.25. Homogeneous graph
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Graph families
10.2.26. Kronecker graph
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Graph families
10.2.27. Lattice graph
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Graph families
10.2.28. Leaf power
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Graph families
10.2.29. Linear forest
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Graph families
10.2.30. List of graphs by edges and vertices
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Graph families
10.2.31. Locally linear graph
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Graph families
10.2.32. Lévy family of graphs
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Graph families
10.2.33. Map graph
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Graph families
10.2.34. Meyniel graph
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Graph families
10.2.35. Modular graph
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Graph families
10.2.36. Multipartite graph
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Graph families
10.2.37. Outerplanar graph
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Graph families
10.2.38. Overfull graph
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Graph families
10.2.39. Pairwise compatibility graph
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Graph families
10.2.40. Panconnectivity
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Graph families
10.2.41. Parity graph
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Graph families
10.2.42. Planar graph
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Graph families
10.2.43. Ptolemaic graph
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Graph families
10.2.44. Quasi-bipartite graph
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Graph families
10.2.45. Scale-free network
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Graph families
10.2.46. Self-complementary graph
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Graph families
10.2.47. Split graph
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Graph families
10.2.48. Squaregraph
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Graph families
10.2.49. Strangulated graph
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Graph families
10.2.50. Strongly chordal graph
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Graph families
10.2.51. Threshold graph
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Graph families
10.2.52. Triangle-free graph
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Graph families
10.2.53. Trivially perfect graph
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Graph families
10.2.54. Universal graph
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Graph families
10.2.55. Well-covered graph
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Graph families
10.2.56. Word-representable graph
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Graph families
10.3. Individual graphs
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Graphs
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10.3.1. 120-cell
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Individual graphs
10.3.2. 26-fullerene graph
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Individual graphs
10.3.3. Berlekamp–Van Lint–Seidel graph
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Individual graphs
10.3.4. Brouwer–Haemers graph
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Individual graphs
10.3.5. Bull graph
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Individual graphs
10.3.6. Butterfly graph
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Individual graphs
10.3.7. Diamond graph
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Individual graphs
10.3.8. Dodecahedron
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Individual graphs
10.3.9. Errera graph
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Individual graphs
10.3.10. Goldner–Harary graph
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Individual graphs
10.3.11. Golomb graph
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Individual graphs
10.3.12. Grötzsch graph
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Individual graphs
10.3.13. Icosahedron
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Individual graphs
10.3.14. Kittell graph
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Individual graphs
10.3.15. Krackhardt kite graph
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Individual graphs
10.3.16. Loupekine snarks
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Individual graphs
10.3.17. M22 graph
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Individual graphs
10.3.18. Moser spindle
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Individual graphs
10.3.19. Octahedron
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Individual graphs
10.3.20. Poussin graph
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Individual graphs
10.3.21. Rado graph
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Individual graphs
10.3.22. Sousselier graph
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Individual graphs
10.3.23. Tetrahedron
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Individual graphs
10.3.24. Truncated icosahedron
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Individual graphs
10.3.25. Truncated icosidodecahedron
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Individual graphs
10.3.26. Truncated tetrahedron
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Individual graphs
10.3.27. Wiener–Araya graph
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Individual graphs
10.4. Infinite graphs
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Graphs
2
10.4.1. Henson graph
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Infinite graphs
10.4.2. Kőnig's lemma
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Infinite graphs
10.5. List of graphs
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Graphs
10.6. Named graph
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Graphs
10.7. Smith graph
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Graphs
10.8. Table of the largest known graphs of a given diameter and maximal degree
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Graphs
11. Random graphs
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Graph theory
23
11.1. Blockmodeling
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Random graphs
11
11.1.1. Andrej Mrvar
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Blockmodeling
11.1.2. Blockmodeling linked networks
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Blockmodeling
11.1.3. Confirmatory blockmodeling
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Blockmodeling
11.1.4. Deterministic blockmodeling
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Blockmodeling
11.1.5. Exploratory blockmodeling
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Blockmodeling
11.1.6. Generalized blockmodeling
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Blockmodeling
11.1.7. Generalized blockmodeling of binary networks
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Blockmodeling
11.1.8. Generalized blockmodeling of valued networks
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Blockmodeling
11.1.9. Harrison White
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Blockmodeling
11.1.10. Implicit blockmodeling
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Blockmodeling
11.1.11. Vladimir Batagelj
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Blockmodeling
11.2. Activity-driven model
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Random graphs
11.3. Erdős–Rényi model
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Random graphs
11.4. Loop-erased random walk
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Random graphs
11.5. Maximum-entropy random graph model
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Random graphs
11.6. Percolation critical exponents
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Random graphs
11.7. Percolation threshold
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Random graphs
11.8. Random geometric graph
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Random graphs
11.9. Random recursive tree
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Random graphs
11.10. Random tree
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Random graphs
11.11. Soft configuration model
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Random graphs
11.12. The Strange Logic of Random Graphs
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Random graphs
12. Unsolved problems in graph theory
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Graph theory
10
12.1. Erdős on Graphs
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Unsolved problems in graph theory
12.2. Erdős–Gyárfás conjecture
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Unsolved problems in graph theory
12.3. Harborth's conjecture
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Unsolved problems in graph theory
12.4. Lovász–Woodall conjecture
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Unsolved problems in graph theory
12.5. Oberwolfach problem
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Unsolved problems in graph theory
12.6. Reconstruction conjecture
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Unsolved problems in graph theory
12.7. Second neighborhood problem
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Unsolved problems in graph theory
12.8. Sumner's conjecture
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Unsolved problems in graph theory
12.9. Szymanski's conjecture
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Unsolved problems in graph theory
12.10. Tuza's conjecture
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Unsolved problems in graph theory
13. Bishop's graph
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Graph theory
14. Blow-up lemma
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Graph theory
15. Boundary (graph theory)
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Graph theory
16. Calculus on finite weighted graphs
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Graph theory
17. Capacitated arc routing problem
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Graph theory
18. Convex subgraph
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Graph theory
19. Copying mechanism
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Graph theory
20. Copying network models
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Graph theory
21. Covering graph
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Graph theory
22. Cycle decomposition (graph theory)
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Graph theory
23. Deficiency (graph theory)
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Graph theory
24. Degree (graph theory)
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Graph theory
25. Deletion–contraction formula
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Graph theory
26. Dense subgraph
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Graph theory
27. Directed graph
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Graph theory
28. Discharging method (discrete mathematics)
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Graph theory
29. Distance oracle
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Graph theory
30. Dominator (graph theory)
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Graph theory
31. Dot product representation of a graph
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Graph theory
32. Eigenvector centrality
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Graph theory
33. Five room puzzle
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Graph theory
34. Flag algebra
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Graph theory
35. Forbidden graph characterization
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Graph theory
36. Fractional graph isomorphism
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Graph theory
37. Frequency partition of a graph
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Graph theory
38. Friendship paradox
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Graph theory
39. Glossary of graph theory
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Graph theory
40. GraphCrunch
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Graph theory
41. Graph (abstract data type)
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Graph theory
42. Graph (discrete mathematics)
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Graph theory
43. Graph Fourier transform
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Graph theory
44. Graph Theory, 1736–1936
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Graph theory
45. Graph amalgamation
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Graph theory
46. Graph canonization
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Graph theory
47. Graph equation
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Graph theory
48. Graph flattenability
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Graph theory
49. Graph property
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Graph theory
50. Graph removal lemma
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Graph theory
51. Graphon
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Graph theory
52. Hall violator
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Graph theory
53. Homeomorphism (graph theory)
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Graph theory
54. Homomorphic equivalence
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Graph theory
55. Hydra game
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Graph theory
56. Hypergraph regularity method
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Graph theory
57. Hypergraph removal lemma
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Graph theory
58. Implicit graph
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Graph theory
59. Incidence poset
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Graph theory
60. Large-scale capacitated arc routing problem
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Graph theory
61. List of graph theory topics
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Graph theory
62. Logic of graphs
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Graph theory
63. Loop (graph theory)
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Graph theory
64. Magic graph
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Graph theory
65. Markov chain
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Graph theory
66. Mixed graph
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Graph theory
67. Nash-Williams theorem
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Graph theory
68. Node influence metric
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Graph theory
69. Null model
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Graph theory
70. Nullity (graph theory)
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Graph theory
71. Pearls in Graph Theory
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Graph theory
72. Pseudorandom graph
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Graph theory
73. Pósa's theorem
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Graph theory
74. Rainbow-independent set
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Graph theory
75. Ramsey-Turán theory
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Graph theory
76. Random graph
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Graph theory
77. Random graph theory of gelation
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Graph theory
78. Random walk closeness centrality
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Graph theory
79. Read's conjecture
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Graph theory
80. Ryser's conjecture
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Graph theory
81. Seven Bridges of Königsberg
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Graph theory
82. Sidorenko's conjecture
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Graph theory
83. Single-entry single-exit
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Graph theory
84. The Mathematics of Chip-Firing
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Graph theory
85. The Petersen Graph
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Graph theory
86. Ultragraph C*-algebra
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Graph theory
87. Vertex (graph theory)
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Graph theory
88. Vertex cover in hypergraphs
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Graph theory
Ancestors
Fields of mathematics
Mathematics
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