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 named graphs in the specified class.

GraphData[n]
gives a list of named graphs with n vertices.

DetailsDetails

  • Graphs can be specified by standard names such as and .
  • 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^(th) 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 standard named graphs with n vertices.
  • GraphData[m;;n] gives a list of standard named graphs with m through n vertices.
  • GraphData["class",n] etc. gives a list of 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:
  • "AdjacencyMatrices"all adjacency matrices
    "AdjacencyMatrix"adjacency matrix
    "AdjacencyMatrixCount"number of distinct adjacency matrices
    "DistanceMatrix"distance matrix
    "EdgeCount"total number of edges
    "EdgeIndices"pairs of vertex indices for each edge
    "EdgeList"edges specified using undirected edges ()
    "EdgeRules"edges specified as vertex connectivity rules
    "FaceCount"total number of faces (for a planar graph)
    "FaceIndices"indices of faces (for a planar graph)
    "IncidenceMatrix"incidence matrix
    "LaplacianMatrix"Laplacian matrix
    "NormalizedLaplacianMatrix"normalized Laplacian matrix
    "VertexCount"total number of vertices
  • Properties related to graph connectivity include:
  • "AlgebraicConnectivity"second smallest eigenvalue of the Laplacian matrix
    "Connected"connected
    "ConnectedComponentCount"number of connected components
    "ConnectedComponentGraphNames"names of graphs induced on connected components
    "ConnectedComponentIndices"indices of connected components
    "Disconnected"disconnected
    "EdgeConnectivity"minimum edge deletions to disconnect the graph
    "Triangulated"triangulated (maximally planar)
    "VertexConnectivity"minimum vertex deletions to disconnect the graph
  • Properties related to graph display include:
  • "AllImages"list of images of all available layouts for the graph
    "AllVertexCoordinates"vertex coordinates for all available layouts
    "EmbeddingClasses"list of embedding class tags, one to an embedding
    "EmbeddingClasses3D"list of 3D embedding class tags, one to a 3D embedding
    "Embeddings"alternate name for "AllVertexCoordinates"
    "Embeddings3D"vertex coordinates for all available 3D layouts
    "Image"image of the default layout
    "Image3D"image embedded in 3D
    "LabeledImage"image of the default layout with vertex numbers included
    "VertexCoordinates"vertex coordinates for the default layout
  • Properties returning Graph objects include:
  • "CanonicalGraph"canonical version of graph that is isomorphic to the original
    "CochromaticGraphs"graphs with the same chromatic polynomial
    "ComplementGraph"graph complement
    "ConnectedComponentGraphs"connected components
    "CoresistanceGraphs"graphs with the same resistance multiset
    "CospectralGraphs"graphs with the same spectrum
    "DualGraph"dual graph
    "Graph"graph object
    "Graph3D"graph object with 3D embedding
    "LineGraph"line graph
    "LocalGraph"local graph
  • GraphData[name,"property","outputtype"] gives graph properties in the format specified by , which, depending on , may be , , , , or , .
  • Annotations related to graph output include:
  • "CayleyGraphGeneratingGroups","outputtype"groups generating graph as a Cayley graph
    "CochromaticGraphs","outputtype"cochromatic graphs
    "ComplementGraph","outputtype"complement graph
    "ConnectedComponentGraphs","outputtype"connected components
    "CoresistanceGraphs","outputtype"coresistance graphs
    "CospectralGraphs","outputtype"cospectral graphs
    "DualGraph","outputtype"dual graph
    "LineGraph","outputtype"line graph
    "LocalGraph","outputtype"local graph
    "PolyhedralEmbeddings","outputtype"polyhedra having given graph as a skeleton
  • GraphData[name,"property","type"] gives a set of specific graphs, images, or embeddings, where in 2D may include , , , , , , , , , , , , , , , and ; and in 3D may include , , , and .
  • Annotations related to graph display include:
  • "Embeddings","type"embeddings of a given type
    "Embeddings3D","type"3D embeddings of a given type
    "Graph","type"graph of a given type
    "Graphs","type"graphs of a given type
    "Graph3D","type"3D-embedded graph of a given type
    "Graphs3D","type"3D-embedded graphs of a given type
    "Images","type"images of a given type
    "Images3D","type"3D images of a given type
  • Properties giving pure functions representing graph polynomials include:
  • "CharacteristicPolynomial"characteristic polynomial of the adjacency matrix
    "ChromaticPolynomial"chromatic polynomial
    "CliquePolynomial"clique polynomial
    "DetourPolynomial"characteristic polynomial of the detour matrix
    "CyclePolynomial"cycle polynomial
    "DistancePolynomial"distance polynomial
    "EdgeCoverPolynomial"edge cover polynomial
    "FlowPolynomial"flow polynomial
    "IdiosyncraticPolynomial"Tutte's idiosyncratic polynomial
    "IndependencePolynomial"independence polynomial
    "LaplacianPolynomial"Laplacian polynomial
    "MatchingGeneratingPolynomial"matching generating polynomial
    "MatchingPolynomial"matching polynomial
    "RankPolynomial"rank polynomial
    "ReliabilityPolynomial"reliability polynomial
    "SigmaPolynomial"chromatic polynomial in falling factorial basis
    "TuttePolynomial"Tutte polynomial
    "VertexCoverPolynomial"vertex cover polynomial
  • Coloringrelated graph properties include:
  • "ChromaticallyUnique"no other graph shares the chromatic polynomial
    "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
    "ZIndex"Z index
  • Local graph properties include:
  • "BridgeCount"number of bridges
    "Bridges"list of edges whose removal would disconnect the graph
    "IsolatedPoints"vertices of degree 0
    "LeafCount"number of leaves
    "Leaves"vertices of degree 1
  • Global graph properties include:
  • "Anarboricity"maximum number of edgedisjoint nonacyclic subgraphs whose union is the original graph
    "Apices"list of vertices whose removal renders the graph planar
    "Arboricity"minimum number of edgedisjoint acyclic subgraphs whose union is the original graph
    "ArticulationVertices"list of vertices whose removal would disconnect the graph
    "Center"indices of vertices with graph eccentrity equal to radius
    "Circumference"circumference of the graph
    "Coarseness"maximum number of linedisjoint nonplanar subgraphs
    "Corank"edge count minus vertex count plus connected component count
    "CrossingNumber"minimum crossings in an embedding of the graph
    "Degrees"degrees for each vertex in vertex order
    "DegreeSequence"vertex degree sorted from smallest to largest
    "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
    "Genus"minimum number of handles to get a planar embedding
    "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
    "RectilinearCrossingNumber"minimum crossings in a straightline embedding
    "ResistanceMatrix"resistances between pairs of vertices for unitresistance edges
    "Skewness"minimum number of edges whose removal would result in a planar graph
    "SpanningTreeCount"number of spanning trees
    "Spectrum"eigenvalues of the adjacency matrix
    "SpectrumSignature"tallies of adjacency matrix eigenvalues
    "Thickness"minimum number of planar subgraphs whose union is the original graph
    "ToroidalCrossingNumber"minimum crossings in a toroidal embedding
  • Cliquerelated properties include:
  • "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
    "CliquePolynomialclique polynomial
    "Cliquescliques
    "FractionalCliqueNumber"fractional clique number
    "MaximalCliqueCount"number of distinct maximal cliques
    "MaximalCliques"maximal cliques
    "MaximalCliqueSignature"tallies of maximal clique sizes
    "MaximumCliqueCount"number of maximum cliques
    "MaximumCliques"maximum cliques
    "MinimumCliqueCoveringCount"number of minimum clique coverings
    "MinimumCliqueCoverings"minimum clique coverings
  • Coverrelated 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
    "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 setrelated properties include:
  • "BipartiteDimension"bipartite dimension
    "ConnectedDominationNumber"smallest possible size of a connected dominating set
    "DominatingSetCount"number of dominating sets
    "DominatingSets"dominating sets
    "DominationNumber"smallest possible size of a dominating set
    "EdgeIndependenceNumber"tallies of independent edge set sizes
    "IndependenceNumber"size of the largest independent vertex set
    "IndependencePolynomial"independence polynomial
    "IndependentEdgeSetCount"number of independent edge sets
    "IndependentEdgeSets"independent edge sets
    "IndependentVertexSetCount"number of independent vertex sets
    "IndependentVertexSets"independent vertex sets
    "IntersectionNumber"intersection number
    "MatchingGeneratingPolynomial"matchinggenerating polynomial
    "MatchingPolynomial"matchinggenerating polynomial
    "MatchingNumber"degree of the matchinggenerating polynomial
    "MaximalIndependentEdgeSetCount"number of maximal independent edge sets (matchings)
    "MaximalIndependentEdgeSets"maximal independent edge sets (matchings)
    "MaximalIndependentEdgeSetSignature"tallies of maximal independent edge set sizes
    "MaximalIndependentVertexSetCount"number of maximal independent vertex sets
    "MaximalIndependentVertexSets"maximal independent vertex sets
    "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
    "MaximumIndependentVertexSetSignature"tallies of maximal independent vertex set sizes
  • Symmetryrelated properties include:
  • "ArcTransitivity"maximal order s of an sarc-transitive 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
  • Informationrelated properties include:
  • "Bandwidth"graph bandwidth
    "CheegerConstant"Cheeger constant
    "Conductance"graph conductance
    "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 graphrepresented communication model
    "TreeDepth"tree depth
    "Treewidth"graph treewidth
  • Path and cyclerelated properties include:
  • "ChordlessCycleSignature"tallies of chordless cycle lengths
    "ChordlessCycles"(simple) cycles with no chords
    "ComplementOddChordlessCycles"odd chordless cycles of the graph complement
    "ComplementOddChordlessCycleSignature"tallies of lengths of odd chordless cycles of the graph complement
    "CyclePolynomial"cycle polynomial
    "DirectedCycleCount"number of distinct directed cycles
    "DirectedCycles"lists of directed cycles
    "DirectedEulerianCycleCount"number of distinct directed Eulerian cycles
    "DirectedEulerianCycles"lists of directed Eulerian cycles
    "DirectedHamiltonianCycleCount"number of distinct directed Hamiltonian cycles
    "DirectedHamiltonianCycles"lists of directed Hamiltonian cycles
    "DirectedHamiltonianPathCount"number of distinct directed Hamiltonian paths
    "DirectedHamiltonianPaths"lists of directed Hamiltonian paths
    "DirectedHamiltonianWalkCount"number of distinct directed Hamiltonian walks
    "DirectedHamiltonianWalks"lists of directed Hamiltonian walks
    "FaceSignature"tallies of face lengths
    "Girth"length of the shortest cycle
    "HamiltonDecompositions"partitions of edge set into Hamiltonian cycles
    "HamiltonianNumber"length of a shortest Hamiltonian walk
    "KCyclicIndices"indices that label the graph as the th -cyclic graph
    "LCFSignature"tally of the orders of all possible LCF signatures
    "OddChordlessCycles"chordless cycles of odd length
    "OddChordlessCycleSignature"tallies of numbers of odd chordless cycles by length
    "Radius"radius of the graph
    "UndirectedCycleCount"number of distinct undirected (simple) cycles
    "UndirectedCycles"lists of undirected (simple) cycles
    "UndirectedEulerianCycleCount"number of distinct undirected (simple) Eulerian cycles
    "UndirectedEulerianCycles"lists of undirected (simple) Eulerian cycles
    "UndirectedHamiltonianCycleCount"number of distinct undirected (simple) Hamiltonian cycles
    "UndirectedHamiltonianCycles"lists of undirected (simple) Hamiltonian cycles
    "UndirectedHamiltonianPathCount"number of distinct undirected (simple) Hamiltonian paths
    "UndirectedHamiltonianPaths"lists of undirected (simple) Hamiltonian paths
    "UndirectedHamiltonianWalkCount"number of distinct undirected (simple) Hamiltonian walks
    "UndirectedHamiltonianWalks"lists of distinct undirected (simple) Hamiltonian walks
  • Namingrelated properties include:
  • "AlternateNames"alternate English names
    "AlternateStandardNames"alternate standard Wolfram Language names
    "CochromaticGraphNames"graphs sharing the same chromatic polynomial
    "ComplementGraphName"name of the complement graph
    "ConnectedComponentGraphNames"graphs making up the connected component
    "CoresistanceGraphNames"graphs sharing the same resistance distance multiset
    "CospectralGraphNames"graphs sharing the same spectrum
    "DualGraphName"name of the graph dual
    "Entity"graph entity
    "LineGraphName"name of the line graph
    "LocalGraphName"name of the local graph
    "Name"English name
    "Names"English name and alternate names
    "StandardName"standard Wolfram Language name
    "StandardNames"standard and alternate Wolfram Language names
  • Notationrelated 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)
    "Planar"planar (no crossings)
    "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 of 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
    "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"Hamiltonconnected with bipartitioned endpoints
    "HStarConnected"either Hamiltonconnected or Hamiltonlaceable
    "Hypohamiltonian"onevertexremoved graphs are Hamiltonian
    "Hypotraceable"onevertexremoved graphs are traceable
    "KempeCounterexample"counterexample to Kempe's 4coloring algorithm
    "MaximallyNonhamiltonian"maximally nonhamiltonian
    "Noneulerian"not Eulerian
    "Nonhamiltonian"not Hamiltonian
    "SquareFree"free of 4cycles
    "Traceable"contains a Hamiltonian path
    "TriangleFree"free of 3cycles
    "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
    "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"vertextransitive 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)
    "Kuratowki"Kuratowki 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
    "ClawFree"free of the claw graph
    "Conference"conference graph
    "CriticalNonplanar"nonplanar and removal of any vertex gives a planar graph
    "Fullerene"planar cubic with all bounded faces pentagons or hexagons
    "Fusene"planar 2connected 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
    "Moore"graphs with the Moore property
    "NoPerfectMatching"has no perfect matching
    "Perfect"perfect graph
    "PerfectMatching"has a matching with n/2 vertices
    "SelfComplementary"isomorphic to its complement
    "SelfDual"isomorphic to its dual
    "Snark"snark graph
    "StronglyPerfect"every induced subgraph H has an independent set meeting all maximal cliques of
    "Toroidal"graph can be 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
  • Graph centralities include:
  • "BetweennessCentralities"betweenness centralities
    "ClosenessCentralities"closeness centrailitities
    "DegreeCentralities"vertex degrees
    "EccentricityCentralities"reciprocal of vertex eccentricities
    "EdgeBetweennessCentralities"edge betweenness centralities
    "EigenvectorCentralities"eigenvector centrailitities
    "HITSCentrailities"hub centrailitities
    "KatzCentralities"Katz centrailitities
    "PageRankCentralities"page rank centrailitities
    "RadialityCentralities"radiality centralities
    "StatusCentralities"status centralities
  • 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
    "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 fourdimensional solids
  • 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 subsets of
    "Book"graph Cartesian product of a star and a twopath graph
    "Bouwer"regular graphs including members that are symmetric but not arc transitive
    "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
    "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
    "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
    "FoldedCube"folded nhypercube graph
    "Gear"a wheel with vertices added between the vertices of the outer cycle
    "GeneralizedPolygon"an incidence plane based on a symmetric binary relation
    "GeneralizedPrism"a generalized (stacked) prism graph
    "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 nhypercube 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
    "Hypercube"an ndimensional hypercube
    "IGraph"generalization of a generalized Petersen graph
    "Johnson"graph describing adjacencies in the msubsets of an nset
    "Keller"Keller graph
    "Kneser"vertices represent ksubsets of
    "Ladder"a vertex ladder graph
    "LadderRung"graph union of n twopaths
    "Lattice"a line graph of the complete bipartite graph
    "MoebiusLadder"an nsided prism graph with a halftwist
    "Mycielski"a trianglefree graph with chromatic number n
    "Odd"an odd graph
    "Paley"graph with vertices adjacent if their difference is a square in
    "Pan"an ncycle connected to a singleton graph by a bridge
    "Path"an nvertex tree with no branches
    "PermutationStar"a "star graph" on permutations of with edges at swaps
    "SierpinskiCarpet"connectivity graph of the Sierpiński carpet
    "SierpinskiSieve"connectivity graph of the Sierpiński sieve
    "Square"vertices represent the ordered pairs of
    "StackedBook"graph Cartesian product of a star and an npath graph
    "Star"a center vertex connected to 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
    "Triangular"an Johnson graph
    "TriangularGrid"a triangular grid graph
    "Turan"a Turán graph on n vertices that is clique free
    "Wheel"a cycle with all vertices connected to a center
    "Windmill"m copies of the complete graph with a vertex in common
  • 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.
Introduced in 2007
(6.0)
| Updated in 2014
(10.0)