Sage Reference Manual: Graph Theory - Mirrors

CHAPTER
ONE
GRAPH OBJECTS AND METHODS
1.1 Generic graphs
This module implements the base class for graphs and digraphs, and methods that can be applied on both. Here is
what it can do:
Basic Graph operations:
networkx_graph()
to_dictionary()
copy()
adjacency_matrix()
incidence_matrix()
distance_matrix()
weighted_adjacency_matrix()
kirchhoff_matrix()
get_boundary()
set_boundary()
has_loops()
allows_loops()
allow_loops()
loops()
has_multiple_edges()
allows_multiple_edges()
allow_multiple_edges()
multiple_edges()
name()
weighted()
antisymmetric()
density()
order()
size()
add_vertex()
add_vertices()
delete_vertex()
delete_vertices()
has_vertex()
random_vertex()
Creates a new NetworkX graph from the Sage graph
Creates a dictionary encoding the graph.
Return a copy of the graph.
Returns the adjacency matrix of the (di)graph.
Returns an incidence matrix of the (di)graph
Returns the distance matrix of the (strongly) connected (di)graph
Returns the weighted adjacency matrix of the graph
Returns the Kirchhoff matrix (a.k.a. the Laplacian) of the graph.
Returns the boundary of the (di)graph.
Sets the boundary of the (di)graph.
Returns whether there are loops in the (di)graph.
Returns whether loops are permitted in the (di)graph.
Changes whether loops are permitted in the (di)graph.
Returns any loops in the (di)graph.
Returns whether there are multiple edges in the (di)graph.
Returns whether multiple edges are permitted in the (di)graph.
Changes whether multiple edges are permitted in the (di)graph.
Returns any multiple edges in the (di)graph.
Returns or sets the graph’s name.
Whether the (di)graph is to be considered as a weighted (di)graph.
Tests whether the graph is antisymmetric
Returns the density
Returns the number of vertices.
Returns the number of edges.
Creates an isolated vertex.
Add vertices to the (di)graph from an iterable container
Deletes a vertex, removing all incident edges.
Remove vertices from the (di)graph taken from an iterable container of vertices.
Return True if vertex is one of the vertices of this graph.
Returns a random vertex of self.
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