Notable simple undirected mathematical graphs.

Entity["Graph",name] or

represents an entity of type "Graph".

[prop]

gives the value of a specified property.

[{propi,}]

gives the value of a list of properties.

EntityClass["Graph",{propispeci,}]

represents a class of entities with values of propi defined by speci.

Sample Entities

Sample Entity Classes

Properties

  • Acyclicacyclic
    AdjacencyListsadjacency lists
    AdjacencyMatricesadjacency matrices
    AdjacencyMatrixadjacency matrix
    AdjacencyMatrixCountadjacency matrix count
    AlgebraicConnectivityalgebraic connectivity
    AlmostHamiltonianalmost Hamiltonian
    AlternateNamesalternate names
    AlternateStandardNamesalternate standard names
    AlternatingGroupalternating group
    Anarboricityanarboricity
    AndrasfaiAndrásfai
    Antelopeantelope
    Antiprismantiprism
    Apexapex
    Apicesapices
    ApollonianApollonian
    Arboricityarboricity
    ArchimedeanArchimedean
    ArchimedeanDualArchimedean dual
    ArcTransitivearctransitive
    ArcTransitivityarctransitivity
    Arrangementarrangement
    ArticulationVertexCountarticulation vertex count
    ArticulationVerticesarticulation vertices
    AssociatedEntitiesassociated entities
    AssociatedPeopleassociated people
    Asymmetricasymmetric
    AutomorphismCountautomorphism group order
    AutomorphismGroupautomorphism group
    BalabanIndexBalaban index
    BananaTreebanana tree
    Bandwidthbandwidth
    Barbellbarbell
    BeinekeBeineke graph
    BetweennessCentralitiesbetweenness centralities
    BicliqueCoverbiclique cover
    Bicolorablebicolorable
    Biconnectedbiconnected
    Bicubicbicubic
    Bipartitebipartite
    BipartiteDimensionbipartite dimension
    BipartiteDoubleGraphbipartite double graph
    BipartiteKneserbipartite Kneser
    Bishopbishop
    BlackBishopblack bishop
    Bookbook
    BouwerBouwer
    BridgeCountbridge count
    Bridgedbridged
    Bridgelessbridgeless
    Bridgesbridges
    BruhatBruhat
    BurningNumberburning number
    Cactuscactus
    Cagecage
    CanonicalFormcanonical form
    CanonicalGraphcanonical graph
    CanonicalStandardNamecanonical standard name
    Caterpillarcaterpillar
    Cavemancaveman
    CayleyCayley
    CayleyGraphGeneratingGroupNamesCayley graph generating group names
    CayleyGraphGeneratingGroupsCayley graph generating groups
    Centercenter
    Centipedecentipede
    ChangChang
    CharacteristicPolynomialcharacteristic polynomial
    CheegerConstantCheeger number
    Chordalchordal
    ChordCountchord count
    Chordlesschordless
    ChordlessCycleCountchordless cycle count
    ChordlessCyclePolynomialchordless cycle polynomial
    ChordlessCycleschordless cycles
    Chordschords
    ChromaticallyNonuniquechromatically nonunique
    ChromaticallyUniquechromatically unique
    ChromaticInvariantchromatic invariant
    ChromaticNumberchromatic number
    ChromaticPolynomialchromatic polynomial
    Circulantcirculant
    Circumferencecircumference
    Class1class 1
    Class2class 2
    Classesclasses
    ClawFreeclawfree
    CliqueCountclique count
    CliqueCoveringNumberclique covering number
    CliqueNumberclique number
    CliquePolynomialclique polynomial
    Cliquescliques
    ClosenessCentralitiescloseness centralities
    Coarsenesscoarseness
    CoboundaryPolynomialcoboundary polynomial
    CochromaticGraphscochromatic graphs
    CocktailPartycocktail party
    ComplementGraphcomplement graph
    ComplementOddChordlessCycleCountcomplement odd chordless cycle count
    ComplementOddChordlessCyclePolynomialcomplement odd chordless cycle polynomial
    ComplementOddChordlessCyclescomplement odd chordless cycles
    Completecomplete
    CompleteBipartitecomplete bipartite
    CompleteKPartitecomplete kpartite
    CompletelyRegularcompletely regular
    CompleteTreecomplete tree
    CompleteTripartitecomplete tripartite
    Conductanceconductance
    Conecone
    Conferenceconference
    Connectedconnected
    ConnectedComponentCountconnected component count
    ConnectedComponentsconnected components
    ConnectedDominatingSetCountconnected dominating set count
    ConnectedDominatingSetsconnected dominating sets
    ConnectedDominationNumberconnected domination number
    ConnectedDominationPolynomialconnected domination polynomial
    ConnectedInducedSubgraphCountconnected induced subgraph count
    ConnectedInducedSubgraphPolynomialconnected induced subgraph polynomial
    Corankcorank
    CoresistanceGraphscoresistance graphs
    CospectralGraphscospectral graphs
    CriticalNonplanarcritical nonplanar
    CrossedPrismcrossed prism
    CrossingNumbercrossing number
    Crowncrown
    CubeConnectedCyclecubeconnected cycle
    Cubiccubic
    Cyclecycle
    CycleCountcycle count
    CyclePolynomialcycle polynomial
    Cyclescycles
    Cycliccyclic
    CyclomaticNumbercyclomatic number
    Cyclotomiccyclotomic
    DegreeCentralitiesdegree centralities
    DegreeSequencedegree sequence
    DeterminedByResistancedetermined by resistance
    DeterminedBySpectrumdetermined by spectrum
    DetourIndexdetour index
    DetourMatrixdetour matrix
    DetourPolynomialdetour polynomial
    DiagonalIntersectiondiagonal intersection
    Diameterdiameter
    Dimensiondimension
    Dipyramiddipyramid
    Disconnecteddisconnected
    DistanceMatrixdistance matrix
    DistancePolynomialdistance polynomial
    DistanceRegulardistanceregular
    DistanceTransitivedistancetransitive
    DistinguishingNumberdistinguishing number
    DomaticNumberdomatic number
    DominatingSetCountdominating set count
    DominatingSetsdominating sets
    DominationNumberdomination number
    DominationPolynomialdomination polynomial
    DoobDoob
    DoubleToroidaldouble toroidal
    DualGraphdual graph
    DualGraphNamedual graph
    DutchWindmillDutch windmill
    Eccentricitieseccentricities
    EccentricityCentralitieseccentricity centralities
    EdgeBetweennessCentralitiesedge betweenness centralities
    EdgeChromaticNumberedge chromatic number
    EdgeConnectivityedge connectivity
    EdgeCountedge count
    EdgeCoverCountedge cover count
    EdgeCoverNumberedge cover number
    EdgeCoverPolynomialedge cover polynomial
    EdgeCoversedge covers
    Edgesedges
    EdgeTransitiveedgetransitive
    EigenvectorCentralitieseigenvector centralities
    EmbeddingClassesembedding classes
    EmbeddingClasses3D3dimensional embedding classes
    Embeddingsembeddings
    Embeddings3Dembeddings 3D
    Emptyempty
    EntityClassesentity classes
    EulerianEulerian
    EulerianCycleCountEulerian cycle count
    EulerianCyclesEulerian cycles
    FaceCountface count
    Facesfaces
    FaceSignatureface signature
    Fanfan
    FibonacciCubefibonacci cube
    Firecrackerfirecracker
    Fiveleaperfiveleaper
    FlowPolynomialflow polynomial
    FoldedCubefolded cube
    Forestforest
    FractionalChromaticNumberfractional chromatic number
    FractionalCliqueNumberfractional clique number
    FractionalEdgeChromaticNumberfractional edge chromatic number
    Fullerenefullerene
    Fusenefusene
    Geargear
    GeneralizedPetersengeneralized Petersen
    GeneralizedPolygongeneralized polygon
    GeneralizedPrismgeneralized prism
    Genusgenus
    Girthgirth
    Gonalitygonality
    Graphgraph object
    Graph3Dgraph object with 3D embedding
    Graphicsgraphic
    GrassmannGrassmann
    Gridgrid
    HaarHaar
    HadamardHadamard
    HalinHalin
    HalvedCubehalved cube
    HamiltonConnectedHamiltonconnected
    HamiltonDecomposableHamilton decomposable
    HamiltonDecompositionCountHamilton decomposition count
    HamiltonDecompositionsHamilton decompositions
    HamiltonianHamiltonian
    HamiltonianCycleCountHamiltonian cycle count
    HamiltonianCyclesHamiltonian cycles
    HamiltonianNumberHamiltonian number
    HamiltonianPathCountHamiltonian path count
    HamiltonianPathsHamiltonian paths
    HamiltonianWalkCountHamiltonian walk count
    HamiltonianWalksHamiltonian walks
    HamiltonLaceableHamiltonlaceable
    HammingHamming
    HanoiHanoi
    HararyHarary
    HararyIndexHarary index
    Helmhelm
    HexagonCounthexagon count
    HITSCentralitiesHITS centralities
    HoneycombToroidalhoneycomb toroidal
    HosoyaIndexHosoya index
    HStarConnectedH^*connected
    Hypercubehypercube
    Hypohamiltonianhypohamiltonian
    Hypotraceablehypotraceable
    Identityidentity
    IdiosyncraticPolynomialidiosyncratic polynomial
    IGraphIgraph
    Imageimage
    Image3D3dimensional image
    Imperfectimperfect
    Incidenceincidence
    IncidenceMatrixincidence matrix
    IndependenceNumberindependence number
    IndependencePolynomialindependence polynomial
    IndependenceRatioindependence ratio
    IndependentEdgeSetCountindependent edge set count
    IndependentEdgeSetsindependent edge sets
    IndependentVertexSetCountindependent vertex set count
    IndependentVertexSetsindependent vertex sets
    Informationhyperlink
    Integralintegral
    IntersectionArrayintersection array
    IntersectionNumberintersection number
    IrredundancePolynomialirredundance polynomial
    IrredundantSetCountirredundant set count
    IrredundantSetsirredundant sets
    IsolatedPointCountisolated point count
    IsolatedPointsisolated points
    JohnsonJohnson
    JohnsonSkeletonJohnson solid skeleton
    KatzCentralitiesKatz centralities
    KCyclicIndiceskcyclic indices
    KellerKeller
    KempeCounterexampleKempe counterexample
    Kingking
    KirchhoffIndexKirchhoff index
    KirchhoffSumIndexKirchhoff sum index
    KleinBottleTriangulationKlein bottle triangulation
    KneserKneser
    Knightknight
    KuratowskiKuratowski
    LabeledImagelabeled image
    Ladderladder
    LadderRungladder rung
    LaplacianMatrixLaplacian matrix
    LaplacianPolynomialLaplacian polynomial
    LaplacianSpectrumLaplacian spectrum
    LaplacianSpectrumSignatureLaplacian spectrum signature
    LCFLCF
    LCFNotationsLCF notations
    LCFSignatureLCF signature
    LeafCountleaf count
    Leavesleaves
    Likelihoodlikelihood
    Lineline
    LineGraphline graph
    LinkRankCentralitieslink rank centralities
    Lobsterlobster
    Locallocal
    LocalGraphlocal graph
    LocallyPetersenlocally Petersen
    Lollipoplollipop
    LongestCycleCountlongest cycle count
    LongestCycleslongest cycles
    LongestPathCountlongest path count
    LongestPathLengthlongest path length
    LongestPathslongest paths
    LovaszNumberLovász number
    MatchingGeneratingPolynomialmatchinggenerating polynomial
    MatchingNumbermatching number
    MatchingPolynomialmatching polynomial
    Matchstickmatchstick
    MaximalCliqueCountmaximal clique count
    MaximalCliquePolynomialmaximal clique polynomial
    MaximalCliquesmaximal cliques
    MaximalIndependencePolynomialmaximal independence polynomial
    MaximalIndependentEdgeSetCountmaximal independent edge set count
    MaximalIndependentEdgeSetsmaximal independent edge sets
    MaximalIndependentVertexSetCountmaximal independent vertex set count
    MaximalIndependentVertexSetsmaximal independent vertex sets
    MaximalIrredundancePolynomialmaximal irredundant set polynomial
    MaximalIrredundantSetCountmaximal irredundant set count
    MaximalIrredundantSetsmaximal irredundant sets
    MaximallyNonhamiltonianmaximally nonhamiltonian
    MaximalMatchingGeneratingPolynomialmaximal matchinggenerating polynomial
    MaximumCliqueCountmaximum clique count
    MaximumCliquesmaximum cliques
    MaximumIndependentEdgeSetCountmaximum independent edge set count
    MaximumIndependentEdgeSetsmaximum independent edge sets
    MaximumIndependentVertexSetCountmaximum independent vertex set count
    MaximumIndependentVertexSetsmaximum independent vertex set
    MaximumIrredundantSetCountmaximum irredundant set count
    MaximumIrredundantSetsmaximum irredundant sets
    MaximumLeafNumbermaximum leaf number
    MaximumVertexDegreemaximum vertex degree
    MeanDistancemean distance
    Medianmedian
    MengerSpongeMenger sponge
    MeshRegionmesh representation
    MetelskyMetelsky
    MinimalConnectedDominatingSetCountminimal connected dominating set count
    MinimalConnectedDominatingSetsminimal connected dominating sets
    MinimalConnectedDominationPolynomialminimal connected domination polynomial
    MinimalDominatingSetCountminimal dominating set count
    MinimalDominatingSetsminimal dominating sets
    MinimalDominationPolynomialminimal domination polynomial
    MinimalEdgeCoverCountminimal edge cover count
    MinimalEdgeCoverPolynomialminimal edge cover polynomial
    MinimalEdgeCoversminimal edge covers
    MinimalMatchingGeneratingPolynomialminimal matchinggenerating set polynomial
    MinimalTotalDominatingSetCountminimal total dominating set count
    MinimalTotalDominatingSetsminimal total dominating sets
    MinimalTotalDominationPolynomialminimal total domination polynomial
    MinimalVertexCoverCountminimal vertex cover count
    MinimalVertexCoverPolynomialminimal vertex cover polynomial
    MinimalVertexCoversminimal vertex covers
    MinimumCliqueCoveringCountminimum coverings by maximal cliques count
    MinimumCliqueCoveringsminimum coverings by maximal cliques
    MinimumConnectedDominatingSetCountminimum connected dominating set count
    MinimumConnectedDominatingSetsminimum connected dominating sets
    MinimumCoveringsByMaximalCliquesminimum coverings by maximal cliques
    MinimumCoveringsByMaximalCliquesCountminimum coverings by maximal cliques count
    MinimumDistinguishingLabelingCountminimum distinguishing labeling count
    MinimumDistinguishingLabelingsminimum distinguishing labelings
    MinimumDominatingSetCountminimum dominating set count
    MinimumDominatingSetsminimum dominating sets
    MinimumEdgeColoringminimum edge coloring
    MinimumEdgeCoverCountminimum edge cover count
    MinimumEdgeCoversminimum edge covers
    MinimumTotalDominatingSetCountminimum total dominating set count
    MinimumTotalDominatingSetsminimum total dominating sets
    MinimumVertexColoringminimum vertex coloring
    MinimumVertexCoverCountminimum vertex cover count
    MinimumVertexCoversminimum vertex covers
    MinimumVertexDegreeminimum vertex degree
    MinimumWeightFractionalColoringminimum weight fractional coloring
    MoebiusLadderMöbius ladder
    MolecularTopologicalIndexmolecular topological index
    MongolianTentMongolian tent
    MooreMoore
    MycielskiMycielski
    Namename
    Noncayleynoncayley
    Nonemptynonempty
    Noneuleriannoneulerian
    Nonhamiltoniannonhamiltonian
    Nonplanarnonplanar
    Nonsimplenonsimple
    NoPerfectMatchinghas no perfect matching
    NormalizedLaplacianMatrixnormalized Laplacian matrix
    Notationnotation
    NotationRulesnotation rules
    NotDeterminedByResistancenot determined by resistance
    NotDeterminedBySpectrumnot determined by spectrum
    Nuciferousnuciferous
    Octicoctic
    Oddodd
    OddChordlessCycleCountodd chordless cycle count
    OddChordlessCyclePolynomialodd chordless cycle polynomial
    OddChordlessCyclesodd chordless cycles
    OreOre
    Outerplanarouterplanar
    PageRankCentralitiesPageRank centralities
    PaleyPaley
    Panpan
    Pancyclicpancyclic
    ParameterConstraintsparameter constraints
    Pathpath
    PathComplementpath complement
    PathCountpath count
    PathPolynomialpath polynomial
    PathPolynomialMatrixpath polynomial matrix
    Pathspaths
    Pathwidthpathwidth
    PaulusPaulus
    PentagonCountpentagon count
    Perfectperfect
    PerfectMatchingperfect matching
    Peripheryperiphery
    PermutationStarpermutation star
    Planarplanar
    PlatonicPlatonic
    Polyhedralpolyhedral
    PolyhedralEmbeddingspolyhedral embeddings
    Polyiamondpolyiamond
    Polyominopolyomino
    Prismprism
    ProjectivePlaneCrossingNumberprojective plane crossing number
    Pseudoforestpseudoforest
    Pseudotreepseudotree
    Quarticquartic
    Queenqueen
    Quinticquintic
    RadialityCentralitiesradiality centralities
    Radiusradius
    Rankrank
    RankPolynomialrank polynomial
    RectilinearCrossingNumberrectilinear crossing number
    Regularregular
    RegularParametersregular parameters
    RegularPolychoronregular polychoron
    ReliabilityPolynomialreliability polynomial
    ResistanceMatrixresistance matrix
    Rookrook
    RookComplementrook complement
    SelfComplementaryselfcomplementary
    SelfDualselfdual
    Semisymmetricsemisymmetric
    Septicseptic
    Sexticsextic
    ShannonCapacityShannon capacity
    SierpinskiCarpetSierpiński carpet
    SierpinskiSieveSierpiński sieve
    SierpinskiTetrahedronSierpiński tetrahedron
    SigmaPolynomialsigma polynomial
    Simplesimple
    Skewnessskewness
    Snarksnark
    SpanningTreeCountspanning tree count
    SpanningTreesspanning trees
    SpectralRadiusspectral radius
    Spectrumspectrum
    SpectrumSignaturespectrum signature
    Spiderspider
    SquareCountsquare count
    SquareFreesquarefree
    StabilityIndexstability index
    StackedBookstacked book
    StackedPrismstacked prism
    Starstar
    StatusCentralitiesstatus centralities
    StronglyConnectedstrongly connected
    StronglyConnectedComponentCountstrongly connected component count
    StronglyConnectedComponentsstrongly connected components
    StronglyPerfectstrongly perfect
    StronglyRegularstrongly regular
    Sunsun
    Sunletsunlet graph
    Symmetricsymmetric
    Tadpoletadpole
    TaylorTaylor
    Tetrahedraltetrahedral
    Thicknessthickness
    TopologicalIndextopological index
    Toroidaltoroidal
    ToroidalCrossingNumbertoroidal crossing number
    TorusGridtorus grid
    TorusTriangulationtorus triangulation
    TotalDominatingSetCounttotal dominating set count
    TotalDominatingSetstotal dominating sets
    TotalDominationNumbertotal domination number
    TotalDominationPolynomialtotal domination polynomial
    Traceabletraceable
    Transpositiontransposition
    Treetree
    TreeDepthtree depth
    Treewidthtreewidth
    Triametertriameter
    TriangleCounttriangle count
    TriangleFreetrianglefree
    Triangulartriangular
    TriangularGridtriangular grid
    TriangularHoneycombAcuteKnighttriangular honeycomb acute knight
    TriangularHoneycombBishoptriangular honeycomb bishop
    TriangularHoneycombKingtriangular honeycomb king
    TriangularHoneycombObtuseKnighttriangular honeycomb obtuse knight
    TriangularHoneycombQueentriangular honeycomb queen
    TriangularHoneycombRooktriangular honeycomb rook
    Triangulatedtriangulated
    Tripodtripod
    TuranTurán
    TuttePolynomialTutte polynomial
    TwoRegulartworegular
    Unicyclicunicyclic
    UnitDistanceunitdistance
    Untraceableuntraceable
    VertexConnectivityvertex connectivity
    VertexCoordinatesvertex coordinates
    VertexCountvertex count
    VertexCoverCountvertex cover count
    VertexCoverNumbervertex cover number
    VertexCoverPolynomialvertex cover polynomial
    VertexCoversvertex covers
    VertexDegreesvertex degrees
    VertexInDegreesvertex indegrees
    VertexOutDegreesvertex outdegrees
    VertexTransitivevertextransitive
    Verticesvertices
    WeaklyConnectedweakly connected
    WeaklyConnectedComponentCountweakly connected component count
    WeaklyConnectedComponentsweakly connected components
    WeaklyPerfectweakly perfect
    WeaklyRegularweakly regular
    Webweb
    WellCoveredwell covered
    Wheelwheel
    WhiteBishopwhite bishop
    WienerIndexWiener index
    WienerSumIndexWiener sum index
    Windmillwindmill
    Wreathwreath
    ZeroSymmetriczerosymmetric
    ZeroTwozerotwo

Details

  • "Graph" entities include particular named simple graphs as well as members of parametrized families.
  • "Graph" entity classes include common mathematical types of graphs, such as "Complete", "Cyclic" and "Planar", together with the negations of some of these.
  • Mathematical properties are available for most "Graph" entities if they are concisely representable and either well known or straightforward to compute. For size reasons, "Graph" entities of given types generally are complete only up to type-dependent vertex count or parameter value. Properties for some parametrized "Graph" entities are available for symbolic parameters.
  • Some properties are available for the "Graph" entity type as a whole and can be given using the form EntityValue["Graph",property]. Such properties include:
  • "Properties"the list of available properties
    "PropertyCanonicalNames"the standard names of available properties
    "SampleEntities"a sample list of available entities (typically of length 10)
    "SampleEntityClasses"a sample list of available entity classes (typically of length 10)
    "EntityCount"number of entities available
    "Entities"the list of available entities
    "EntityCanonicalNames"the standard names of available entities
    "EntityClasses"the list of available entity classes
    "EntityClassCanonicalNames"the standard names of available entity classes
    "PropertyClasses"the list of available property classes
    "PropertyClassCanonicalNames"the standard names of available property classes
    "PropertyCount"number of properties available
  • The following annotations can be used in the third argument of EntityValue["Graph",property,annotation]:
  • "Source"source information for the property
    "Date"the date associated with the entity-property value (if any)
    "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values
    "EntityPropertyAssociation"an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "PropertyEntityAssociation"an association in which the specified properties are keys, and values are a nested association of entities and entity-property values
    "Dataset"a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
  • The following annotations can be used in the second argument of EntityValue[property,annotation]:
  • "Qualifiers"the list of possible qualifiers for the property
    "QualifierValues"the list of possible values that can be given to each qualifier
    "DefaultQualifierValues"the list of default values for the property's qualifiers
    "Description"a brief textual description of the property
    "Definition"a detailed textual definition of the property
    "PhysicalQuantity"the physical quantity associated with the entity-property value
    "Unit"the unit associated with the entity-property value
  • A qualifier value of Automatic indicates that an applicable format of values can be used; e.g. for the "Date" qualifier, this includes a proper date or date span.

Examples

Basic Examples  (3)

Use for entity discovery:

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Find a property value for an entity:

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Retrieve a dataset of all available properties for an entity:

In[1]:=
Click for copyable input
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