| "ArticulationVertices" | list of vertices whose removal would disconnect the graph |

| "AutomorphismCount" | order of the vertex automorphism group |

| "Automorphisms" | vertex permutations corresponding to automorphisms |

| "Bridges" | list of edges whose removal would disconnect the graph |

| "ChromaticNumber" | chromatic number |

| "ChromaticPolynomial" | chromatic polynomial as a pure function |

| "CliqueNumber" | number of vertices in the largest clique |

| "CrossingNumber" | minimum crossings in an embedding of the graph |

| "Degrees" | degrees for each vertex |

| "Diameter" | the diameter of the graph |

| "Eccentricities" | eccentricities of each vertex |

| "EdgeChromaticNumber" | edge chromatic number |

| "EdgeConnectivity" | minimum edge deletions to disconnect the graph |

| "Girth" | length of the shortest cycle |

| "HamiltonianCycleCount" | number of distinct Hamiltonian cycles |

| "HamiltonianCycles" | lists of Hamiltonian cycles |

| "HamiltonianPathCount" | number of distinct Hamiltonian paths |

| "HamiltonianPaths" | lists of Hamiltonian paths |

| "IndependenceNumber" | size of the largest independent set |

| "LineGraphName" | name of the line graph corresponding to the graph |

| "RectilinearCrossingNumber" | minimum crossings in a straight line embedding |

| "Spectrum" | eigenvalues of the adjacency matrix |

| "ToroidalCrossingNumber" | minimum crossings in a toroidal embedding |

| "VertexConnectivity" | minimum vertex deletions to disconnect the graph |