Sage Reference Manual: Graph Theory - Mirrors

Sage Reference Manual: Graph Theory, Release 6.1.1
sage: D = DiGraph( { 0: [1,2,3], 1: [4,5], 2: [5], 3: [6], 5: [7], 6: [7], 7: [0]})
sage: list(D.breadth_first_search(5,neighbors=D.neighbors_in, distance=2))
[5, 1, 2, 0]
sage: list(D.breadth_first_search(5,neighbors=D.neighbors_out, distance=2))
[5, 7, 0]
sage: list(D.breadth_first_search(5,neighbors=D.neighbors, distance=2))
[5, 1, 2, 7, 0, 4, 6]
TESTS:
sage: D = DiGraph({1:[0], 2:[0]})
sage: list(D.breadth_first_search(0))
[0]
sage: list(D.breadth_first_search(0, ignore_direction=True))
[0, 1, 2]
canonical_label(partition=None, certify=False, verbosity=0, edge_labels=False)
Returns the unique graph on {0, 1, ..., n − 1} ( n = self.order() ) which
•is isomorphic to self,
•is invariant in the isomorphism class.
In other words, given two graphs G and H which are isomorphic, suppose G_c and H_c are the graphs
returned by canonical_label. Then the following hold:
•G_c == H_c
•G_c.adjacency_matrix() == H_c.adjacency_matrix()
•G_c.graph6_string() == H_c.graph6_string()
INPUT:
•partition - if given, the canonical label with respect to this set partition will be computed. The
default is the unit set partition.
•certify - if True, a dictionary mapping from the (di)graph to its canonical label will be given.
•verbosity - gets passed to nice: prints helpful output.
•edge_labels - default False, otherwise allows only permutations respecting edge labels.
EXAMPLES:
sage: D = graphs.DodecahedralGraph()
sage: E = D.canonical_label(); E
Dodecahedron: Graph on 20 vertices
sage: D.canonical_label(certify=True)
(Dodecahedron: Graph on 20 vertices, {0: 0, 1: 19, 2: 16, 3: 15, 4: 9, 5: 1, 6: 10, 7: 8, 8:
sage: D.is_isomorphic(E)
True
Multigraphs:
sage: G = Graph(multiedges=True,sparse=True)
sage: G.add_edge((0,1))
sage: G.add_edge((0,1))
sage: G.add_edge((0,1))
sage: G.canonical_label()
Multi-graph on 2 vertices
sage: Graph(’A’, implementation=’c_graph’).canonical_label()
Graph on 2 vertices
1.1. Generic graphs 21