Sage Reference Manual: Graph Theory - Mirrors

Sage Reference Manual: Graph Theory, Release 6.1.1
cartesian_product()
tensor_product()
lexicographic_product()
strong_product()
disjunctive_product()
Paths and cycles:
Returns the Cartesian product of self and other.
Returns the tensor product, also called the categorical product, of self and other.
Returns the lexicographic product of self and other.
Returns the strong product of self and other.
Returns the disjunctive product of self and other.
eulerian_orientation() Returns a DiGraph which is an Eulerian orientation of the current graph.
eulerian_circuit()Return a list of edges forming an eulerian circuit if one exists.
cycle_basis() Returns a list of cycles which form a basis of the cycle space of self.
interior_paths() Returns an exhaustive list of paths (also lists) through only interior vertices from vertex
start to vertex end in the (di)graph.
all_paths() Returns a list of all paths (also lists) between a pair of vertices in the (di)graph.
triangles_count() Returns the number of triangles in the (di)graph.
Linear algebra:
spectrum()
eigenvectors()
eigenspaces()
Some metrics:
Returns a list of the eigenvalues of the adjacency matrix.
Returns the right eigenvectors of the adjacency matrix of the graph.
Returns the right eigenspaces of the adjacency matrix of the graph.
cluster_triangles() Returns the number of triangles for nbunch of vertices as a dictionary keyed by
vertex.
clustering_average() Returns the average clustering coefficient.
clustering_coeff() Returns the clustering coefficient for each vertex in nbunch
cluster_transitivity() Returns the transitivity (fraction of transitive triangles) of the graph.
szeged_index()
Returns the Szeged index of the graph.
Automorphism group:
coarsest_equitable_refinement()
Returns the coarsest partition which is finer than the input partition, and equitable
with respect to self.
automorphism_group() Returns the largest subgroup of the automorphism group of the (di)graph whose
orbit partition is finer than the partition given.
is_vertex_transitive() Returns whether the automorphism group of self is transitive within the partition
provided
is_isomorphic() Tests for isomorphism between self and other.
canonical_label() Returns the unique graph on {0, 1, ..., n − 1} ( n = self.order() ) which 1)
is isomorphic to self 2) is invariant in the isomorphism class.
Graph properties:
is_eulerian()
is_planar()
is_circular_planar()
is_regular()
is_chordal()
is_circulant()
is_interval()
is_gallai_tree()
is_clique()
is_independent_set()
is_transitively_reduced()
is_equitable()
Traversals:
Return true if the graph has a (closed) tour that visits each edge exactly once.
Tests whether the graph is planar.
Tests whether the graph is circular planar (outerplanar)
Return True if this graph is (k-)regular.
Tests whether the given graph is chordal.
Tests whether the graph is a circulant graph.
Check whether self is an interval graph
Returns whether the current graph is a Gallai tree.
Tests whether a set of vertices is a clique
Tests whether a set of vertices is an independent set
Tests whether the digraph is transitively reduced.
Checks whether the given partition is equitable with respect to self.
1.1. Generic graphs 3