GraphData
GraphData[name]
gives a graph with the specified name.
GraphData[name,"property"]
gives the value for the specified property for a named graph.
GraphData["class"]
gives a list of available named graphs in the specified class.
GraphData[n]
gives a list of available named graphs with n vertices.
Details
 Graphs can be specified by standard names such as "PetersenGraph" and "FosterCage".
 GraphData[patt] gives a list of all graph names that match the string pattern patt.
 GraphData[] gives a list of all standard named graphs. GraphData[All] gives all available graphs.
 GraphData[name] gives a Graph object.
 GraphData[{n,i},…] gives data for the i simple graph with n vertices.
 GraphData[{"type",id},…] gives data for the graph of the specified type with identifier id. The identifier is typically an integer or lists of integers.
 GraphData[;;n] gives a list of available standard named graphs with ≤n vertices.
 GraphData[m;;n] gives a list of available standard named graphs with m through n vertices.
 GraphData["class",n] etc. gives a list of available graphs with n vertices etc. in the specified class.
 GraphData["Classes"] gives a list of all supported classes.
 GraphData["Properties"] gives a list of properties available for graphs.
 Basic graph properties include:

"AdjacencyMatrix" adjacency matrix "AdjacencyMatrixCount" number of distinct adjacency matrices "DistanceMatrix" distance matrix "EdgeCount" total number of edges "Edges" edges "FaceCount" total number of faces (for a planar graph) "Faces" faces "IncidenceMatrix" incidence matrix "LaplacianMatrix" Laplacian matrix "NormalizedLaplacianMatrix" normalized Laplacian matrix "VertexCount" total number of vertices "Vertices" vertices  Properties related to graph connectivity include:

"AlgebraicConnectivity" second smallest eigenvalue of the Laplacian matrix "ArticulationVertices" list of vertices whose removal would disconnect the graph "BridgeCount" number of bridges "Bridges" list of edges whose removal would disconnect the graph "Connected" connected "ConnectedComponentCount" number of connected components "ConnectedInducedSubgraphCount" connected induced subgraph count "ConnectedComponents" connected components "Disconnected" disconnected "EdgeConnectivity" minimum edge deletions to disconnect the graph "SpanningTrees" spanning trees "Triangulated" triangulated (maximally planar) "VertexConnectivity" minimum vertex deletions to disconnect the graph  Properties related to graph display include:

"EmbeddingClasses" list of embedding class tags, one to an embedding "Embeddings" vertex coordinates for all available layouts "Graph" graph object "Graphics" graphic "Graphics3D" 3D graphics "Image" image "MeshRegion" mesh region "VertexCoordinates" vertex coordinates for the default layout  Properties returning Graph objects include:

"BipartiteDoubleGraph" bipartite double graph "CanonicalGraph" canonical version of graph that is isomorphic to the original "CochromaticGraphs" graphs with the same chromatic polynomial "ComplementGraph" graph complement "ConnectedComponents" connected components "CoresistanceGraphs" graphs with the same resistance multiset "CospectralGraphs" graphs with the same spectrum "DualGraph" dual graph "Graph" graph object "LineGraph" line graph "LocalGraph" local graph  Annotatable properties related to listtype output include:

"AdjacencyMatrix","outputtype" one or all adjacency matrices or count of all possible adjacency matrices "Cycles","outputtype" undirected, directed, or count of cycles "Edges","outputtype" edges as a list, edge list, index pair list, rule list, graphic, or count of edges "EulerianCycles","outputtype" undirected, directed, or count of Eulerian cycles "Faces","outputtype" faces as a list, index list, graphic, or count of faces "HamiltonianCycles","outputtype" undirected, directed, or count of Hamiltonian cycles "HamiltonianPaths","outputtype" undirected, directed, or count of Hamiltonian paths "HamiltonianWalks","outputtype" undirected, directed, or count of Hamiltonian walks "VertexCoordinates","outputtype" one or all vertex coordinates or embedding count "Vertices","outputtype" vertices as a list, indexed coordinate rule list, graphic, or count of vertices  Properties giving pure functions representing graph polynomials include:

"CharacteristicPolynomial" characteristic polynomial of the adjacency matrix "ChordlessCyclePolynomial" polynomial encoding the counts of chordless cycles by length "ChromaticPolynomial" chromatic polynomial "CliquePolynomial" clique polynomial "CoboundaryPolynomial" coboundary polynomial "ComplementOddChordlessCyclePolynomial" polynomial encoding the counts of odd chordless cycles in the graph complement by length "ConnectedDominationPolynomial" connected domination polynomial "ConnectedInducedSubgraphPolynomial" polynomial encoding the counts of connected induced subgraphs by size "CyclePolynomial" cycle polynomial "DetourPolynomial" characteristic polynomial of the detour matrix "DistancePolynomial" distance polynomial "DominationPolynomial" domination polynomial "EdgeCoverPolynomial" edge cover polynomial "FlowPolynomial" flow polynomial "IdiosyncraticPolynomial" Tutte's idiosyncratic polynomial "IndependencePolynomial" independence polynomial "IrredundancePolynomial" irredundance polynomial "LaplacianPolynomial" Laplacian polynomial "MatchingGeneratingPolynomial" matching generating polynomial "MatchingPolynomial" matching polynomial "MaximalCliquePolynomial" polynomial encoding the counts of maximal cliques by size "MaximalIndependencePolynomial" polynomial encoding the counts of maximal independent vertex sets by size "MaximalIrredundancePolynomial" polynomial encoding the counts of maximal irredundant sets by size "MaximalMatchingGeneratingPolynomial" polynomial encoding the counts of maximal independent edge sets by size "MinimalConnectedDominationPolynomial" polynomial encoding the counts of minimal connected dominating sets by size "MinimalDominationPolynomial" polynomial encoding the counts of minimal dominating sets by size "MinimalEdgeCoverPolynomial" polynomial encoding the counts of minimal edge covers by size "MinimalTotalDominationPolynomial" polynomial encoding the counts of minimal total dominating sets by size "MinimalVertexCoverPolynomial" polynomial encoding the counts of minimal vertex covers by size "OddChordlessCyclePolynomial" polynomial encoding the counts of odd chordless cycles by length "PathPolynomial" path polynomial "RankPolynomial" rank polynomial "ReliabilityPolynomial" reliability polynomial "SigmaPolynomial" chromatic polynomial in falling factorial basis "TotalDominationPolynomial" polynomial encoding the counts of total dominating sets by size "TuttePolynomial" Tutte polynomial "VertexCoverPolynomial" vertex cover polynomial  Coloring‐related graph properties include:

"ChromaticInvariant" chromatic invariant "ChromaticNumber" chromatic number "EdgeChromaticNumber" edge chromatic number "FractionalChromaticNumber" fractional chromatic number "FractionalEdgeChromaticNumber" fractional edge chromatic number "MinimumVertexColoring" minimum vertex coloring "MinimumEdgeColoring" minimum edge coloring "MinimumWeightFractionalColoring" minimum weight fractional coloring  Graph index properties include:

"BalabanIndex" Balaban index "CyclomaticNumber" minimum number of edges to remove to turn acyclic "DetourIndex" detour index "HararyIndex" Harary index "HosoyaIndex" Hosoya index "KirchhoffIndex" Kirchhoff index "KirchhoffSumIndex" Kirchhoff sum index "MolecularTopologicalIndex" molecular topological (second Schultz) index "StabilityIndex" stability index "TopologicalIndex" topological (first Schultz) index "WienerIndex" Wiener index "WienerSumIndex" Wiener sum index  Local graph properties include:

"ChordCount" number of chords "Chords" chords "IsolatedPoints" vertices of degree 0 "LeafCount" number of leaves "Leaves" vertices of degree 1  Global graph properties include:

"Anarboricity" maximum number of edge‐disjoint nonacyclic subgraphs whose union is the original graph "Apices" list of vertices whose removal renders the graph planar "Arboricity" minimum number of edge‐disjoint acyclic subgraphs whose union is the original graph "Center" indices of vertices with graph eccentricity equal to radius "Circumference" circumference of the graph "Coarseness" maximum number of line‐disjoint nonplanar subgraphs "Corank" edge count minus vertex count plus connected component count "DegreeSequence" vertex degrees in monotonic nonincreasing order "DeterminedByResistance" no other graph shares the same multiset of resistances "DeterminedBySpectrum" no other graph shares the spectrum "DetourMatrix" matrix of longest path distances "Diameter" diameter of the graph "Eccentricities" eccentricities of each vertex "LaplacianSpectrum" eigenvalues of the Laplacian matrix "MaximumLeafNumber" largest number of tree leaves in any spanning trees "MaximumVertexDegree" largest vertex degree "MeanDistance" mean distance between vertices "MinimumVertexDegree" smallest vertex degree "Periphery" indices of vertices with graph eccentricity equal to diameter "Rank" vertex count minus connected component count "ResistanceMatrix" resistances between pairs of vertices for unit‐resistance edges "Skewness" minimum number of edges whose removal would result in a planar graph "SpanningTreeCount" number of spanning trees "SpectralRadius" spectral radius "Spectrum" eigenvalues of the adjacency matrix "SpectrumSignature" tallies of adjacency matrix eigenvalues "Thickness" minimum number of planar subgraphs whose union is the original graph "Triameter" graph triameter (generalization of graph diameter) "VertexDegrees" vertex degeres  Topological graph properties include:

"CrossingNumber" minimum crossings in an embedding of the graph "Genus" minimum number of handles yielding a nonedgecrossing embedding "KleinBottleCrossigNumber" minimum crossings in a Klein bottle embedding "ProjectivePlaneCrossingNumber" minimum crossings in a projective plane embedding "RectilinearCrossingNumber" minimum crossings in a straight‐line embedding "ToroidalCrossingNumber" minimum crossings in a toroidal embedding  Clique‐related properties include:

"CliquePolynomial clique polynomial "Cliques cliques "BicliqueNumber" biclique number "BipartiteDimension" bipartite dimension "CliqueCount" number of cliques "CliqueCoveringNumber" minimum number of maximum cliques needed to cover the vertex set "CliqueNumber" number of vertices in a maximum clique "FractionalCliqueNumber" fractional clique number "MaximalCliqueCount" number of distinct maximal cliques "MaximalCliquePolynomial" polynomial encoding tallies of maximal clique sizes "MaximalCliques" maximal cliques "MaximumCliqueCount" number of maximum cliques "MaximumCliques" maximum cliques "MinimumCoveringsByMaximalCliques" smallest coverings by maximal cliques "MinimumCoveringsByMaximalCliquesCount" number of smallest coverings by maximal cliques  Cover‐related properties include:

"CliqueCoveringNumber" minimum number of maximum cliques needed to cover the vertex set "EdgeCoverCount" number of edge covers "EdgeCoverNumber" size of the minimum edge cover "EdgeCoverPolynomial" edge cover polynomial "EdgeCovers" edge covers "MinimalEdgeCoverCount" number of minimal edge covers "MinimalEdgeCoverPolynomial" polynomial encoding tallies of minimal edge cover sizes "MinimalEdgeCovers" minimal edge covers "MinimalVertexCoverCount" number of minimal vertex covers "MinimalVertexCoverPolynomial" polynomial encoding tallies of minimal vertex cover sizes "MinimalVertexCovers" minimal vertex covers "MinimumCliqueCoveringCount" number of minimum clique coverings "MinimumCliqueCoverings" minimum clique coverings "MinimumEdgeCoverCount" number of minimum edge covers (matchings) "MinimumEdgeCovers" minimum edge covers (matchings) "MinimumVertexCoverCount" number of minimum vertex covers "MinimumVertexCovers" minimum vertex covers "VertexCoverCount" number of vertex covers "VertexCoverNumber" size of a minimum vertex cover "VertexCoverPolynomial" vertex cover polynomial  Independent set‐related properties include:

"BipartiteDimension" bipartite dimension "EdgeIndependenceNumber" tallies of independent edge set sizes "IndependenceNumber" size of the largest independent vertex set "IndependencePolynomial" independence polynomial "IndependenceRatio" independence ratio "IndependentEdgeSetCount" number of independent edge sets "IndependentEdgeSets" independent edge sets "IndependentVertexSetCount" number of independent vertex sets "IndependentVertexSets" independent vertex sets "IntersectionNumber" intersection number "MatchingGeneratingPolynomial" matching‐generating polynomial "MatchingNumber" degree of the matching‐generating polynomial "MatchingPolynomial" matching‐generating polynomial "MaximalIndependencePolynomial" polynomial encoding the numbers of maximal independent vertex sets by size "MaximalIndependentEdgeSetCount" number of maximal independent edge sets (matchings) "MaximalIndependentEdgeSets" maximal independent edge sets (matchings) "MaximalIndependentVertexSetCount" number of maximal independent vertex sets "MaximalIndependentVertexSets" maximal independent vertex sets "MaximalMatchingGeneratingPolynomial" polynomial encoding the numbers of maximal independent edge sets by size "MaximumIndependentEdgeSetCount" number of maximum independent edge sets (matchings) "MaximumIndependentEdgeSets" maximum independent edge sets (matchings) "MaximumIndependentVertexSetCount" number of maximum independent vertex sets "MaximumIndependentVertexSets" maximum independent vertex sets  Irredundant set‐related properties include:

"IrredundantSetCount" number of irredundant sets "IrredundantSets" irredundant sets "MaximalIrredundancePolynomial" polynomial encoding tallies of maximal irredundant set sizes "MaximalIrredundantSetCount" number of maximal irredundant sets "MaximalIrredundantSets" maximal irredundant sets "MaximumIrredundantSetCount" number of maximum irredundant sets "MaximumIrredundantSets" maximum irredundant sets  Dominating set‐related properties include:

"ConnectedDominatingSetCount" connected dominating set count "ConnectedDominatingSets" connected dominating sets "ConnectedDominationNumber" size of smallest possible connected dominating set "ConnectedDominationPolynomial" polynomial encoding tallies of connected dominating set sizes "DomaticNumber" maximum number of disjoint dominating sets in a domatic partition of a graph "DominatingSetCount" number of dominating sets "DominatingSets" dominating sets "DominationNumber" size of smallest possible dominating set "DominationPolynomial" polynomial encoding tallies of dominating set sizes "MinimalConnectedDominatingSetCount" number of minimal connected dominating sets "MinimalConnectedDominatingSets" minimal connected dominating sets "MinimalConnectedDominationPolynomial" polynomial encoding tallies of minimal connected dominating set sizes "MinimalDominatingSetCount" number of minimal dominating sets "MinimalDominatingSets" minimal dominating sets "MinimalDominationPolynomial" polynomial encoding tallies of minimal dominating set sizes "MinimalTotalDominatingSetCount" number of minimal total dominating sets "MinimalTotalDominatingSets" minimal total dominating sets "MinimalTotalDominationPolynomial" polynomial encoding tallies of minimal total dominating set sizes "MinimumConnectedDominatingSetCount" minimum connected dominating set count "MinimumConnectedDominatingSets" minimum connected dominating sets "MinimumDominatingSetCount" number of minimum dominating sets "MinimumDominatingSets" minimum dominating sets "MinimumTotalDominatingSetCount" number of minimum total dominating sets "MinimumTotalDominatingSets" minimum total dominating sets "TotalDominatingSetCount" number of total dominating sets "TotalDominatingSets" total dominating sets "TotalDominationNumber" size of smallest possible total dominating set "TotalDominationPolynomial" polynomial encoding the tallies of total dominating set sizes  Symmetry‐related properties include:

"ArcTransitivity" maximal order s of an s‐arctransitive graph "AutomorphismCount" order of the vertex automorphism group "AutomorphismGroup" graph automorphism permutation group "CayleyGraphGeneratingGroupNames" names of groups that generate the graph as a Cayley graph "CayleyGraphGeneratingGroups" groups that generate the graph as a Cayley graph "DistinguishingNumber" distinguishing number "MinimumDistinguishingLabelingCount" number of minimum distinguishing labelings "MinimumDistinguishingLabelings" minimum distinguishing labelings  Information‐related properties include:

"Bandwidth" graph bandwidth "BurningNumber" burning number "CheegerConstant" Cheeger constant "Conductance" graph conductance "Gonality" gonality "Likelihood" probability for graph to be generated by random number and corresponding vertex subset picking "LovaszNumber" Lovász number (estimate of Shannon capacity) "Pathwidth" graph pagewidth "ShannonCapacity" effective alphabet size in a graph‐represented communication model "TreeDepth" tree depth "Treewidth" graph treewidth  Path‐ and cycle‐related properties include:

"ChordlessCycleCount" number of chordless cycles "ChordlessCyclePolynomial" polynomial encoding tallies of chordless cycle lengths "ChordlessCycles" cycles with no chords "ComplementOddChordlessCycleCount" number of odd chordless cycles in the graph complement "ComplementOddChordlessCyclePolynomial" polynomial encoiding tallies of lengths of odd chordless cycles of the graph complement "ComplementOddChordlessCycles" odd chordless cycles in the graph complement "CycleCount" number of distinct cycles "CyclePolynomial" cycle polynomial "Cycles" lists of cycles "EulerianCycleCount" number of distinct Eulerian cycles "EulerianCycles" lists of Eulerian cycles "FaceSignature" tallies of face lengths "Girth" length of the shortest cycle "HamiltonDecompositionCount" number of Hamilton decompositions "HamiltonDecompositions" partitions of edge set into Hamiltonian cycles "HamiltonianCycleCount" number of distinct Hamiltonian cycles "HamiltonianCycles" lists of Hamiltonian cycles "HamiltonianNumber" length of a shortest Hamiltonian walk "HamiltonianPathCount" number of distinct Hamiltonian paths "HamiltonianPaths" lists of Hamiltonian paths "HamiltonianWalkCount" number of distinct Hamiltonian walks "HamiltonianWalks" lists of Hamiltonian walks "HexagonCount" number of 6cycles "KCyclicIndices" indices that label the graph as the th cyclic graph "LCFSignature" tally of the orders of all possible LCF signatures "LongestCycleCount" number of longest cycles "LongestCycles" longest cycles "LongestPathCount" number of longest paths "LongestPathLength" length of longest path "LongestPaths" longest paths "OddChordlessCycleCount" number of odd chordless cycles "OddChordlessCyclePolynomial" polynomial encoding tallies of numbers of odd chordless cycles by length "OddChordlessCycles" chordless cycles of odd length "PathCount" number of distinct paths "PathPolynomial" path polynomial "PathPolynomialMatrix" matrix function of path polynomials "Paths" lists of paths "PentagonCount" number of 5cycles "Radius" radius of the graph "SquareCount" number of 4cycles "TriangleCount" number of 3cycles  Graph centralities include:

"BetweennessCentralities" betweenness centralities "ClosenessCentralities" closeness centralities "DegreeCentralities" vertex degrees "EccentricityCentralities" reciprocal of vertex eccentricities "EdgeBetweennessCentralities" edge betweenness centralities "EigenvectorCentralities" eigenvector centralities "HITSCentralities" hub centralities "KatzCentralities" Katz centralities "LinkRankCentralities" link rank centralities "PageRankCentralities" page rank centralities "RadialityCentralities" radiality centralities "StatusCentralities" status centralities  Naming‐related properties include:

"AlternateNames" alternate English names "AlternateStandardNames" alternate standard Wolfram Language names "Entity" graph entity "Name" English name "Names" English name and alternate names "StandardName" standard Wolfram Language name "StandardNames" standard and alternate Wolfram Language names  Notation‐related properties include:

"LCFNotations" graph notations for embeddings based on Hamiltonian cycles "Notation" primary notation used for graph "NotationRules" rules for notations specifying the graph  GraphData["class"] gives a list of named graphs in the specified class. GraphData[name,"class"] gives True or False, depending on whether the graph corresponding to name is in the specified class.
 GraphData[name,"Classes"] gives a list of the classes in which the graph corresponding to name appears.
 Basic classes of graphs include:

"Bipartite" bipartite (two components connected by every edge) "Nonplanar" nonplanar (requires crossings) "Nonsimple" nonsimple graph "Planar" planar (no crossings) "Simple" simple graph (unlabeled, undirected) "Tree" tree (no cycles)  Classes based on vertex degrees include:

"Cubic" each vertex is of degree 3 "Octic" each vertex is of degree 8 "Quartic" each vertex is of degree 4 "Quintic" each vertex is of degree 5 "Regular" each vertex is of the same degree "Septic" each vertex is of degree 7 "Sextic" each vertex is of degree 6 "TwoRegular" each vertex is of degree 2  Classes based on traversals include:

"Acyclic" free of cycles "AlmostHamiltonian" node graph with Hamiltonian number "Bridged" contains at least one bridge "Bridgeless" free of bridges "Chordal" free of chordless cycles "Chordless" free of chords "Cyclic" contains at least one cycle "Eulerian" has a closed cycle containing every edge once "HamiltonConnected" every pair of vertices bounds a Hamiltonian path "HamiltonDecomposable" has a partition of its edge set into Hamiltonian cycles "Hamiltonian" has a closed cycle containing every vertex once "HamiltonLaceable" Hamilton‐connected with bipartitioned endpoints "HStarConnected" either Hamilton‐connected or Hamilton‐laceable "Hypohamiltonian" one‐vertex‐removed graphs are Hamiltonian "Hypotraceable" one‐vertex‐removed graphs are traceable "KempeCounterexample" counterexample to Kempe's 4‐coloring algorithm "MaximallyNonhamiltonian" maximally nonhamiltonian "Median" median graph "Noneulerian" not Eulerian "Nonhamiltonian" not Hamiltonian "Pancyclic" contains cycles of all lengths from 3 to vertex count "SquareFree" free of 4‐cycles "Traceable" contains a Hamiltonian path "TriangleFree" free of 3‐cycles "Unicyclic" possesses a single cycle "Untraceable" not traceable  Classes based on chess boards include:

"Antelope" moves of an antelope generalized chess piece "Bishop" moves of two (white and black) chess bishops "BlackBishop" moves of a chess black bishop "Fiveleaper" moves of a fiveleaper generalized chess piece "King" moves of a chess king "Knight" moves of a chess knight "Queen" moves of a chess queen "Rook" moves of a chess rook "RookComplement" graph complement of a rook graph "TriangularHoneycombAcuteKnight" moves of an acute knight on a triangular honeycomb chess board "TriangularHoneycombBishop" moves of a bishop on a triangular honeycomb chess board "TriangularHoneycombKing" moves of a king on a triangular honeycomb chess board "TriangularHoneycombObtuseKnight" moves of an obtuse knight on a triangular honeycomb chess board "TriangularHoneycombQueen" moves of a queen on a triangular honeycomb chess board "TriangularHoneycombRook" moves of a rook on a triangular honeycomb chess board "WhiteBishop" moves of a chess white bishop  Classes based on symmetry and regularity include:

"ArcTransitive" ordered pairs of adjacent vertices have identical environments "Asymmetric" not symmetric "Chang" strongly regular on 28 vertices "DistanceRegular" all vertices have identical distance sets "DistanceTransitive" all pairs of vertices have identical distance environments "EdgeTransitive" all edges have identical environments "Identity" automorphism group is of order unity "LocallyPetersen" locally Petersen "Paulus" strongly regular on 25 or 26 vertices "Semisymmetric" regular and edge transitive but not vertex transitive "StronglyRegular" strongly regular "Symmetric" both edge transitive and vertex transitive "Taylor" distance regular with intersection array of form "VertexTransitive" all vertices have identical environments "WeaklyRegular" regular, but not strongly regular "ZeroSymmetric" vertex‐transitive cubic with edges partitioned into three orbits "ZeroTwo" every two vertices have either 0 or 2 common neighbors  Classes based on forbidden graphs include:

"Beineke" Beineke graph (not a line graph if these are forbidden) "Kuratowski" Kuratowski graph ( or ) "Metelsky" Metelsky graph (not a line graph if these are forbidden and )  Special classes include:

"Apex" apex graph "Bicolorable" two or fewer vertex colors needed "Bicubic" bipartite and cubic "Cage" smallest graph of a given girth "Cayley" Cayley graph "ChromaticallyUnique" no other graph shares the chromatic polynomial "ClawFree" free of the claw graph "Conference" conference graph "CriticalNonplanar" nonplanar and removal of any vertex gives a planar graph "DoubleToroidal" graph can be minimally emebdded on a double torus "Fullerene" planar cubic with all bounded faces pentagons or hexagons "Fusene" planar 2‐connected with all bounded faces hexagons "Imperfect" imperfect (i.e. not perfect) graph "Incidence" incidence graph of a configuration "Integral" spectrum consists of integers "LCF" describable in LCF notation (regular Hamiltonian) "Line" line graph "Local" graph is locally a particular graph for all vertices "Matchstick" embeddable with a planar drawing having unit edge lengths "Moore" graphs with the Moore property "Nonempty" nonempty graph "NoPerfectMatching" has no perfect matching "Nuciferous" nuciferous graph "Ore" Ore graph "Perfect" perfect graph "PerfectMatching" has a matching with vertices "SelfComplementary" isomorphic to its complement "SelfDual" isomorphic to its dual "Snark" snark graph "StronglyPerfect" every induced subgraph has an independent set meeting all maximal cliques of "Toroidal" graph can be minimally embedded on a torus "UnitDistance" embeddable with edges of unit length "WeaklyPerfect" clique number equals chromatic number "WellCovered" every minimal vertex cover has the same size  Classes associated with polyhedra include:

"Antiprism" skeleton of an antiprism "Archimedean" skeleton of one of the 13 Archimedean solids "ArchimedeanDual" skeleton of one of the 13 Archimedean duals "Dipyramid" skeleton of a dipyramid "JohnsonSkeleton" skeleton of one of the 92 Johnson solids "Platonic" skeleton of one of the five Platonic solids "Polyhedral" skeleton of a polyhedron "Prism" skeleton of a prism "RegularPolychoron" skeleton of one of the six regular four‐dimensional solids "Wheel" skeleton of a pyramid  Special classes of trees and their generalization include:

"Cactus" connected graph in which any two graph cycles have no edge in common "Caterpillar" vertices are on a central stalk or only one edge away from a stalk "Centipede" vertices and edges correspond to the configuration of a comb "Forest" a collection of trees (same as "Acyclic") "Halin" Halin graph "Lobster" removal of leaves gives a caterpillar "Pseudoforest" contains at most one cycle per connected component "Pseudotree" a connected pseudoforest "Spider" one vertex of degree at most 3 and all others with degree at most 2 "Tripod" a tree having exactly three tree leaves  Classes of graphs indexed by one or more integers include:

"Apollonian" connectivity graph of a 2D Apollonian gasket "BipartiteKneser" vertices represent k subsets and n‐k subsets of {1,…,n} "Book" graph Cartesian product of a star and a two‐path graph "Bouwer" regular graphs including members that are symmetric but not arc transitive "Bruhat" graph whose vertices are permutations on n symbols with edges for permutations differing by an adjacent transposition "Caveman" caveman graph "Circulant" n vertices each with identical relative adjacencies "Complete" all pairs of vertices are connected "CompleteBipartite" all pairs connected across two disjoint sets of vertices "CompleteKPartite" all pairs connected across disjoint sets of vertices "CompleteTripartite" all neighboring pairs connected across three disjoint sets of vertices "Cone" graph join of a cycle graph and empty graph "Crown" complete bipartite with horizontal edges removed "Cycle" a single cycle through n vertices "Cyclotomic" graph with vertices adjacent if their difference is a cube in "DiagonalIntersection" graph with vertices formed from the vertices of a regular ngon and the intersection of its diagonals "Dipyramid" skeleton graph of an ndipyramid "Doob" Cartesian product of Shrikhande graphs and a Hamming graph "Empty" n vertices with no edges "Fan" graph join of an empty graph with a path graph "FibonacciCube" a Fibonacci cube graph "FoldedCube" folded n‐hypercube graph "Gear" a wheel with vertices added between the vertices of the outer cycle "GeneralizedPolygon" an incidence plane based on a symmetric binary relation "Grid" an array of points with grid connectivity "Haar" Haar (regular bipartite) graph of index n "Hadamard" graph corresponding to a matrix satisfying "HalvedCube" halved n‐hypercube graph "Hamming" direct product of m complete graphs of size n "Hanoi" a Hanoi graph "Harary" a Harary graph "Helm" a wheel with a pendant edge adjoined at each cycle vertex "HoneycombToroidal" honeycomb toroidal graph "Hypercube" an n‐dimensional hypercube "IGraph" generalization of a generalized Petersen graph "Johnson" graph describing adjacencies in the m‐subsets of an n‐set "JohnsonSkeleton" skeleton graph of the n Johnson solid "Keller" Keller graph "KleinBottleTriangulation" a regular triangulation of a Klein bottle "Kneser" vertices represent k‐subsets of {1,…,n} "Ladder" a 2n‐vertex ladder graph "LadderRung" graph union of n two‐paths "MoebiusLadder" an n‐sided prism graph with a half‐twist "MengerSponge" connectivity graph of a Menger sponge "Mycielski" a triangle‐free graph with chromatic number n "Odd" an odd graph "Paley" graph with vertices adjacent if their difference is a square in "Pan" an n‐cycle connected to a singleton graph by a bridge "Path" an n‐vertex tree with no branches "PathComplement" complement graph of the npath graph "PermutationStar" a "star graph" on permutations of {1,…,n} with edges at swaps "SierpinskiCarpet" connectivity graph of the Sierpiński carpet "SierpinskiSieve" connectivity graph of the Sierpiński sieve "SierpinskiTetrahedron" connectivity graph of the Sierpiński tetrahedron (tetrix) "StackedBook" graph Cartesian product of a star and a path graph "StackedPrism" a stacked prism graph "Star" a center vertex connected to n‐1 vertices "Sun" a complete graph with erected triangles on outer edges "Sunlet" a cycle with pendant edges "Tetrahedral" an ‐Johnson graph "TorusGrid" grid graph on a torus "TorusTriangulation" a regular triangulation of a torus "Transposition" a transposition graph "Triangular" an ‐Johnson graph "TriangularGrid" a triangular grid graph "Turan" a Turán graph on n vertices that is (k+1)‐clique free "Wheel" a cycle with all vertices connected to a center "Windmill" m copies of the complete graph with a vertex in common "Wreath" n collections of k nodes arranged around a circle such that all nodes in adjacent collections are connected  GraphData[name,"property","type"] gives a set of specific graphs, images, or embeddings, where in 2D "type" may include "3D", "All", "Circulant", "Circular", "Degenerate", "Gear", "GeneralizedPetersen", "Grid", "Halin", "IGraph", "IntegerCoordinates", "Integral", "LCF", "Linear", "Matchstick", "MinimalCrossing", "MinimalIntegral", "MinimalPlanarIntegral", "MinimalRectilinearCrossing", "Perspective", "Planar", "Polyiamond", "Polyomino", "Primary", "Torus", "TriangularGrid", "UnitDistance", and "XYZ"; and in 3D "type" may include "Grid", "IntegerCoordinates", "Integral", "Polyhedron", "Primary", "TetrahedralGrid", "UnitDistance", and "XYZ".
 Type properties related to graph display include:

"Embeddings" embeddings of a given type "EmbeddingClasses" list of embedding classifications "Graph" graph of a given type "Graphics" graphics "Graphics3D" 3D graphics "Image" images of a given type "MeshRegion" mesh region  GraphData[name,"property","outputtype"] gives graph properties in the format specified by "outputtype", which, depending on "property", may be "All", "Count", "Directed", "Edge", "Entity", "Graph", "Graphics", "Group", "Image", "Labeled", "List", "Name", "Pair", "Polyhedron", "Rule", or "Undirected".
 Output type properties related to graph output include:

"CayleyGraphGeneratingGroups" groups generating corresponding to graph as a Cayley graph as groups, entities, or entity names "CochromaticGraphs" cochromatic graphs as graphs, entities, entity names, 3D graphs, graphics, or images "ComplementGraph" complement graph as a graph, entitiy, entity name, graphics, or image "ConnectedComponents" connected components as graphs, entities, entity names, 3D graphs, graphics, or images "CoresistanceGraphs" coresistance graphs as graphs, entities, entity names, 3D graphs, graphics, or images "CospectralGraphs" cospectral graphs as graphs, entities, entity names, 3D graphs, graphics, or images "DualGraph" dual graph as a graph, entitiy, entity name, graphics, or image "LineGraph" line graph as a graph, entitiy, entity name, graphics, or image "LocalGraph" local graph as a graph, entitiy, entity name, graphics, or image "PolyhedralEmbeddings" polyhedra having given graph as a skeleton as polyhedra, entities, or entity names  GraphData[name,"property","ann"] or GraphData["property","ann"] gives various annotations associated with a property. Typical annotations include:

"Description" short textual description of the property "Information" hyperlink to additional information "LongDescription" longer textual description of the property "Note" additional information about the property "Value" the value of the property  Using GraphData may require internet connectivity.
Examples
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Introduced in 2007
Updated in 2019
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