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ZooGraph

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Janoš Vidali edited this page Dec 20, 2015 · 1 revision

The ZooGraph class

This class is the main class for all simple undirected graph objects. Its methods and properties should be relevant to all simple undirected graphs.

Properties

  • automorphism_group (ZooGroup) - the automorphism group of the graph
  • average_degree (rational) - the average degree of the vertices of the graph
  • average_distance (rational) - the average distance between vertices of the graph
  • chromatic_index (integer) - the chromatic index of the graph
  • chromatic_number (integer) - the chromatic number of the graph
  • clique_number (integer) - the clique number of the graph
  • cluster_transitivity (rational) - the transitivity of the graph
  • clustering_average (rational) - the average clustering index of the graph
  • connected_components_number (integer) - the number of connected components
  • data (text) - graph data in graph6, sparse6, auto6 or some other format
    • The above formats are distinguished by the first character. If other formats are to be supported, an additional field specifying the format may be required.
    • The data should give the graph for some canonical labelling. A field determining which labelling has been used will be necessary.
  • density (rational) - the density of the graph
  • diameter (integer) - the diameter of the graph
    • A special value (infinity or -1) should be used for disconnected graphs.
  • edge_connectivity (integer) - the edge connectivity of the graph
  • fractional_chromatic_index (integer) - the fractional chromatic index of the graph
  • genus (integer) - the minimal genus of the graph
  • girth (integer) - the girth of the graph
  • has_multiple_edges (boolean) - true if the graph has multiple edges between a pair of vertices
  • is_arc_transitive (boolean) - true if the graph is arc-transitive
  • is_asteroidal_triple_free (boolean) - true if the graph has no asteroidal triples
  • is_bipartite (boolean) - true if the graph is bipartite
  • is_cartesian_product (boolean) - true if the graph is a cartesian product
  • is_cayley (boolean) - true if the graph is distance-transitive
  • is_chordal (boolean) - true if the graph is chordal
  • is_circulant (boolean) - true if the graph is circulant
  • is_circular_planar (boolean) - true if the graph is circular planar
  • is_distance_regular (boolean) - true if the graph is distance-regular
  • is_distance_transitive (boolean) - true if the graph is distance-transitive
  • is_edge_transitive (boolean) - true if the graph is edge-transitive
  • is_eulerian (boolean) - true if the graph is Eulerian
  • is_even_hole_free (boolean) - true if the graph has no even holes
  • is_forest (boolean) - true if the graph is a forest
  • is_gallai_tree (boolean) - true if the graph is a Gallai tree
  • is_hamiltonian (boolean) - true if the graph is Hamiltonian
  • is_interval (boolean) - true if the graph is an interval graph
  • is_line_graph (boolean) - true if the graph is a line graph
  • is_long_antihole_free (boolean) - true if the graph has no antiholes of size at least 5
  • is_long_hole_free (boolean) - true if the graph has no holes of size at least 5
  • is_odd_hole_free (boolean) - true if the graph has no odd holes
  • is_overfull (boolean) - true if the graph is overfull
  • is_perfect (boolean) - true if the graph is perfect
  • is_prime (boolean) - true if the graph is prime
  • is_regular (boolean) - true if the graph is regular
  • is_split (boolean) - true if the graph is a split graph
  • is_strongly_regular (boolean) - true if the graph is strongly regular
  • is_tree (boolean) - true if the graph is a tree
  • is_vertex_transitive (boolean) - true if the graph is vertex-transitive
  • lovasz_theta (real) - the Lovász number of the graph
  • maximum_average_degree (rational) - the average degree of the densest subgraph
  • name (text) - a common name for the graph
  • number_of_loops (integer) - the number of loops
  • odd_girth (integer) - the odd girth of the graph
  • order (integer) - the order of the graph (i.e., the number of vertices)
  • radius (integer) - the radius of the graph
  • size (integer) - the number of edges
  • spanning_trees_count (integer) - the number of spanning trees
  • szeged_index (integer) - the Szeged index of the graph
  • triangles_count (integer) - the number of triangles
  • treewidth (integer) - the tree-width of the graph
  • vertex_connectivity (integer) - the vertex connectivity of the graph
  • wiener_index (integer) - the Wiener index of the graph
  • zagreb1_index (integer) - the first Zagreb index of the graph
  • zagreb2_index (integer) - the second Zagreb index of the graph
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