Sage Reference Manual: Graph Theory - Mirrors

Sage Reference Manual: Graph Theory, Release 6.1.1
sage: g = digraphs.ButterflyGraph(3)
sage: g.plot()
You can also use the collection of pre-defined graphs, then create a digraph from them.
sage: g = DiGraph(graphs.PetersenGraph())
sage: g.plot()
Calling Digraph on a graph returns the original graph in which every edge is replaced by two different edges
going toward opposite directions.
In order to obtain more information about these digraph constructors, access the documentation by typing
digraphs.RandomDirectedGNP.
Once you have defined the digraph you want, you can begin to work on it by using the almost 200 functions on
graphs and digraphs in the Sage library! If your digraph is named g, you can list these functions as previously
this way
•Within a Sage session, type g. (Do not press “Enter”, and do not forget the final period ”.” )
•Hit “tab”.
As usual, you can get some information about what these functions do by typing (e.g. if you want to know about
the diameter() method) g.diameter.
If you have defined a digraph g having several connected components ( i.e. g.is_connected() returns
False ), you can print each one of its connected components with only two lines:
sage: for component in g.connected_components():
... g.subgraph(component).plot()
The same methods works for strongly connected components
sage: for component in g.strongly_connected_components():
... g.subgraph(component).plot()
INPUT:
•data - can be any of the following (see the format keyword):
1.A dictionary of dictionaries
2.A dictionary of lists
3.A numpy matrix or ndarray
4.A Sage adjacency matrix or incidence matrix
5.A pygraphviz graph
6.A SciPy sparse matrix
7.A NetworkX digraph
•pos - a positioning dictionary: for example, the spring layout from NetworkX for the 5-cycle is:
{0: [-0.91679746, 0.88169588],
1: [ 0.47294849, 1.125 ],
2: [ 1.125 ,-0.12867615],
3: [ 0.12743933,-1.125 ],
4: [-1.125 ,-0.50118505]}
•name - (must be an explicitly named parameter, i.e., name=”complete”) gives the graph a name
•loops - boolean, whether to allow loops (ignored if data is an instance of the DiGraph class)
1.3. Directed graphs 237