Sage Reference Manual: Graph Theory - Mirrors

Sage Reference Manual: Graph Theory, Release 6.1.1
•vertices - If vertices is a single vertex, returns the number of neighbors of vertex. If vertices is an
iterable container of vertices, returns a list of degrees. If vertices is None, same as listing all vertices.
•labels - see OUTPUT
OUTPUT: Single vertex- an integer. Multiple vertices- a list of integers. If labels is True, then returns a
dictionary mapping each vertex to its degree.
EXAMPLES:
sage: P = graphs.PetersenGraph()
sage: P.degree(5)
3
sage: K = graphs.CompleteGraph(9)
sage: K.degree()
[8, 8, 8, 8, 8, 8, 8, 8, 8]
sage: D = DiGraph( { 0: [1,2,3], 1: [0,2], 2: [3], 3: [4], 4: [0,5], 5: [1] } )
sage: D.degree(vertices = [0,1,2], labels=True)
{0: 5, 1: 4, 2: 3}
sage: D.degree()
[5, 4, 3, 3, 3, 2]
degree_histogram()
Returns a list, whose ith entry is the frequency of degree i.
EXAMPLES:
sage: G = graphs.Grid2dGraph(9,12)
sage: G.degree_histogram()
[0, 0, 4, 34, 70]
sage: G = graphs.Grid2dGraph(9,12).to_directed()
sage: G.degree_histogram()
[0, 0, 0, 0, 4, 0, 34, 0, 70]
degree_iterator(vertices=None, labels=False)
Returns an iterator over the degrees of the (di)graph.
In the case of a digraph, the degree is defined as the sum of the in-degree and the out-degree, i.e. the total
number of edges incident to a given vertex.
INPUT:
•labels (boolean) – if set to False (default) the method returns an iterator over degrees. Otherwise
it returns an iterator over tuples (vertex, degree).
•vertices - if specified, restrict to this subset.
EXAMPLES:
sage: G = graphs.Grid2dGraph(3,4)
sage: for i in G.degree_iterator():
... print i
3
4
2
...
2
4
sage: for i in G.degree_iterator(labels=True):
1.1. Generic graphs 35