Graph plotting

(For LaTeX drawings of graphs, see the graph_latex module.)

All graphs have an associated Sage graphics object, which you can display:

sage: G = graphs.WheelGraph(15)
sage: P = G.plot()
sage: P.show()  # long time

>>> from sage.all import *
>>> G = graphs.WheelGraph(Integer(15))
>>> P = G.plot()
>>> P.show()  # long time

G = graphs.WheelGraph(15)
P = G.plot()
P.show()  # long time
../../_images/graph_plot-1.svg

When plotting a graph created using Sage’s Graph command, node positions are determined using the spring-layout algorithm. Special graphs available from graphs.* have preset positions. For example, compare the two plots of the Petersen graph, as obtained using Graph or as obtained from that database:

sage: petersen_spring = Graph(':I`ES@obGkqegW~')
sage: petersen_spring.show()  # long time

>>> from sage.all import *
>>> petersen_spring = Graph(':I`ES@obGkqegW~')
>>> petersen_spring.show()  # long time

petersen_spring = Graph(':I`ES@obGkqegW~')
petersen_spring.show()  # long time
../../_images/graph_plot-2.svg 
sage: petersen_database = graphs.PetersenGraph()
sage: petersen_database.show()  # long time

>>> from sage.all import *
>>> petersen_database = graphs.PetersenGraph()
>>> petersen_database.show()  # long time

petersen_database = graphs.PetersenGraph()
petersen_database.show()  # long time
../../_images/graph_plot-3.svg

All constructors in this database (except some random graphs) prefill the position dictionary, bypassing the spring-layout positioning algorithm.

Plot options

Here is the list of options accepted by plot() and the constructor of GraphPlot. Those two functions also accept all options of sage.plot.graphics.Graphics.show().

layout

A layout algorithm – one of : “acyclic”, “circular” (plots the graph with vertices evenly distributed on a circle), “ranked”, “graphviz”, “planar”, “spring” (traditional spring layout, using the graph’s current positions as initial positions), or “tree” (the tree will be plotted in levels, depending on minimum distance for the root).

iterations

The number of times to execute the spring layout algorithm.

heights

A dictionary mapping heights to the list of vertices at this height.

spring

Use spring layout to finalize the current layout.

tree_root

A vertex designation for drawing trees. A vertex of the tree to be used as the root for the layout='tree' option. If no root is specified, then one is chosen close to the center of the tree. Ignored unless layout='tree'.

forest_roots

An iterable specifying which vertices to use as roots for the layout='forest' option. If no root is specified for a tree, then one is chosen close to the center of the tree. Ignored unless layout='forest'.

tree_orientation

The direction of tree branches – ‘up’, ‘down’, ‘left’ or ‘right’.

save_pos

Whether or not to save the computed position for the graph.

dim

The dimension of the layout – 2 or 3.

prog

Which graphviz layout program to use – one of “circo”, “dot”, “fdp”, “neato”, or “twopi”.

by_component

Whether to do the spring layout by connected component – boolean.

pos

The position dictionary of vertices.

vertex_labels

Vertex labels to draw. This can be True/False to indicate whether to print the vertex string representation of not, a dictionary keyed by vertices and associating to each vertex a label string, or a function taking as input a vertex and returning a label string.

vertex_color

Default color for vertices not listed in vertex_colors dictionary.

vertex_colors

A dictionary specifying vertex colors: each key is a color recognizable by matplotlib, and each corresponding value is a list of vertices.

vertex_size

The size to draw the vertices.

vertex_shape

The shape to draw the vertices. Currently unavailable for Multi-edged DiGraphs.

edge_labels

Whether or not to draw edge labels.

edge_style

The linestyle of the edges. It should be one of “solid”, “dashed”, “dotted”, dashdot”, or “-”, “–”, “:”, “-.”, respectively.

edge_thickness

The thickness of the edges.

edge_color

The default color for edges not listed in edge_colors.

edge_colors

A dictionary specifying edge colors: each key is a color recognized by matplotlib, and each corresponding value is a list of edges.

color_by_label

Whether to color the edges according to their labels. This also accepts a function or dictionary mapping labels to colors.

partition

A partition of the vertex set. If specified, plot will show each cell in a different color; vertex_colors takes precedence.

loop_size

The radius of the smallest loop.

dist

The distance between multiedges.

max_dist

The max distance range to allow multiedges.

talk

Whether to display the vertices in talk mode (larger and white).

graph_border

Whether or not to draw a frame around the graph.

edge_labels_background

The color of the background of the edge labels.

Default options

This module defines two dictionaries containing default options for the plot() and show() methods. These two dictionaries are sage.graphs.graph_plot.DEFAULT_PLOT_OPTIONS and sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS, respectively.

Obviously, these values are overruled when arguments are given explicitly.

Here is how to define the default size of a graph drawing to be (6, 6). The first two calls to show() use this option, while the third does not (a value for figsize is explicitly given):

sage: import sage.graphs.graph_plot
sage: sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (6, 6)
sage: graphs.PetersenGraph().show()  # long time
sage: graphs.ChvatalGraph().show()  # long time
sage: graphs.PetersenGraph().show(figsize=(4, 4))  # long time

>>> from sage.all import *
>>> import sage.graphs.graph_plot
>>> sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (Integer(6), Integer(6))
>>> graphs.PetersenGraph().show()  # long time
>>> graphs.ChvatalGraph().show()  # long time
>>> graphs.PetersenGraph().show(figsize=(Integer(4), Integer(4)))  # long time

import sage.graphs.graph_plot
sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (6, 6)
graphs.PetersenGraph().show()  # long time
graphs.ChvatalGraph().show()  # long time
graphs.PetersenGraph().show(figsize=(4, 4))  # long time

We can now reset the default to its initial value, and now display graphs as previously:

sage: sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (4, 4)
sage: graphs.PetersenGraph().show()  # long time
sage: graphs.ChvatalGraph().show()  # long time

>>> from sage.all import *
>>> sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (Integer(4), Integer(4))
>>> graphs.PetersenGraph().show()  # long time
>>> graphs.ChvatalGraph().show()  # long time

sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (4, 4)
graphs.PetersenGraph().show()  # long time
graphs.ChvatalGraph().show()  # long time

Note

  • While DEFAULT_PLOT_OPTIONS affects both G.show() and G.plot(), settings from DEFAULT_SHOW_OPTIONS only affects G.show().

  • In order to define a default value permanently, you can add a couple of lines to Sage’s startup scripts. Example:

    sage: import sage.graphs.graph_plot
sage: sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (4, 4)

    >>> from sage.all import *
>>> import sage.graphs.graph_plot
>>> sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (Integer(4), Integer(4))

    import sage.graphs.graph_plot
sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = (4, 4)

Index of methods and functions

GraphPlot.set_pos()

Set the position plotting parameters for this GraphPlot.

GraphPlot.set_vertices()

Set the vertex plotting parameters for this GraphPlot.

GraphPlot.set_edges()

Set the edge (or arrow) plotting parameters for the GraphPlot object.

GraphPlot.show()

Show the (Di)Graph associated with this GraphPlot object.

GraphPlot.plot()

Return a graphics object representing the (di)graph.

GraphPlot.layout_tree()

Compute a nice layout of a tree.
class sage.graphs.graph_plot.GraphPlot(graph, options)[source]

Bases: SageObject

Return a GraphPlot object, which stores all the parameters needed for plotting (Di)Graphs.

A GraphPlot has a plot and show function, as well as some functions to set parameters for vertices and edges. This constructor assumes default options are set. Defaults are shown in the example below.

EXAMPLES:

sage: from sage.graphs.graph_plot import GraphPlot
sage: options = {
....:     'vertex_size': 200,
....:     'vertex_labels': True,
....:     'layout': None,
....:     'edge_style': 'solid',
....:     'edge_color': 'black',
....:     'edge_colors': None,
....:     'edge_labels': False,
....:     'iterations': 50,
....:     'tree_orientation': 'down',
....:     'heights': None,
....:     'graph_border': False,
....:     'talk': False,
....:     'color_by_label': False,
....:     'partition': None,
....:     'dist': .075,
....:     'max_dist': 1.5,
....:     'loop_size': .075,
....:     'edge_labels_background': 'transparent'}
sage: g = Graph({0: [1, 2], 2: [3], 4: [0, 1]})
sage: GP = GraphPlot(g, options)

>>> from sage.all import *
>>> from sage.graphs.graph_plot import GraphPlot
>>> options = {
...     'vertex_size': Integer(200),
...     'vertex_labels': True,
...     'layout': None,
...     'edge_style': 'solid',
...     'edge_color': 'black',
...     'edge_colors': None,
...     'edge_labels': False,
...     'iterations': Integer(50),
...     'tree_orientation': 'down',
...     'heights': None,
...     'graph_border': False,
...     'talk': False,
...     'color_by_label': False,
...     'partition': None,
...     'dist': RealNumber('.075'),
...     'max_dist': RealNumber('1.5'),
...     'loop_size': RealNumber('.075'),
...     'edge_labels_background': 'transparent'}
>>> g = Graph({Integer(0): [Integer(1), Integer(2)], Integer(2): [Integer(3)], Integer(4): [Integer(0), Integer(1)]})
>>> GP = GraphPlot(g, options)

from sage.graphs.graph_plot import GraphPlot
options = {
    'vertex_size': 200,
    'vertex_labels': True,
    'layout': None,
    'edge_style': 'solid',
    'edge_color': 'black',
    'edge_colors': None,
    'edge_labels': False,
    'iterations': 50,
    'tree_orientation': 'down',
    'heights': None,
    'graph_border': False,
    'talk': False,
    'color_by_label': False,
    'partition': None,
    'dist': .075,
    'max_dist': 1.5,
    'loop_size': .075,
    'edge_labels_background': 'transparent'}
g = Graph({0: [1, 2], 2: [3], 4: [0, 1]})
GP = GraphPlot(g, options)
layout_tree(root, orientation)[source]

Compute a nice layout of a tree.

INPUT:

  • root – the root vertex

  • orientation – whether to place the root at the top or at the bottom:

    • orientation="down" – children are placed below their parent

    • orientation="top" – children are placed above their parent

EXAMPLES:

sage: from sage.graphs.graph_plot import GraphPlot
sage: G = graphs.HoffmanSingletonGraph()
sage: T = Graph()
sage: T.add_edges(G.min_spanning_tree(starting_vertex=0))
sage: T.show(layout='tree', tree_root=0)  # indirect doctest

>>> from sage.all import *
>>> from sage.graphs.graph_plot import GraphPlot
>>> G = graphs.HoffmanSingletonGraph()
>>> T = Graph()
>>> T.add_edges(G.min_spanning_tree(starting_vertex=Integer(0)))
>>> T.show(layout='tree', tree_root=Integer(0))  # indirect doctest

from sage.graphs.graph_plot import GraphPlot
G = graphs.HoffmanSingletonGraph()
T = Graph()
T.add_edges(G.min_spanning_tree(starting_vertex=0))
T.show(layout='tree', tree_root=0)  # indirect doctest
plot(**kwds)[source]

Return a graphics object representing the (di)graph.

INPUT:

The options accepted by this method are to be found in the documentation of the sage.graphs.graph_plot module, and the show() method.

Note

See the module's documentation for information on default values of this method.

We can specify some pretty precise plotting of familiar graphs:

sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000': [0, 5], '#FF9900': [1, 6], '#FFFF00': [2, 7],
....:      '#00FF00': [3, 8], '#0000FF': [4,9]}
sage: pos_dict = {}
sage: for i in range(5):
....:  x = float(cos(pi/2 + ((2*pi)/5)*i))
....:  y = float(sin(pi/2 + ((2*pi)/5)*i))
....:  pos_dict[i] = [x,y]
...
sage: for i in range(5, 10):
....:  x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
....:  y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
....:  pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()

>>> from sage.all import *
>>> from math import sin, cos, pi
>>> P = graphs.PetersenGraph()
>>> d = {'#FF0000': [Integer(0), Integer(5)], '#FF9900': [Integer(1), Integer(6)], '#FFFF00': [Integer(2), Integer(7)],
...      '#00FF00': [Integer(3), Integer(8)], '#0000FF': [Integer(4),Integer(9)]}
>>> pos_dict = {}
>>> for i in range(Integer(5)):
...  x = float(cos(pi/Integer(2) + ((Integer(2)*pi)/Integer(5))*i))
...  y = float(sin(pi/Integer(2) + ((Integer(2)*pi)/Integer(5))*i))
...  pos_dict[i] = [x,y]
...
>>> for i in range(Integer(5), Integer(10)):
...  x = float(RealNumber('0.5')*cos(pi/Integer(2) + ((Integer(2)*pi)/Integer(5))*i))
...  y = float(RealNumber('0.5')*sin(pi/Integer(2) + ((Integer(2)*pi)/Integer(5))*i))
...  pos_dict[i] = [x,y]
...
>>> pl = P.graphplot(pos=pos_dict, vertex_colors=d)
>>> pl.show()

from math import sin, cos, pi
P = graphs.PetersenGraph()
d = {'#FF0000': [0, 5], '#FF9900': [1, 6], '#FFFF00': [2, 7],
     '#00FF00': [3, 8], '#0000FF': [4,9]}
pos_dict = {}
for i in range(5):
 x = float(cos(pi/2 + ((2*pi)/5)*i))
 y = float(sin(pi/2 + ((2*pi)/5)*i))
 pos_dict[i] = [x,y]
for i in range(5, 10):
 x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
 y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
 pos_dict[i] = [x,y]
pl = P.graphplot(pos=pos_dict, vertex_colors=d)
pl.show()
../../_images/graph_plot-4.svg

Here are some more common graphs with typical options:

sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0,
....:                 graph_border=True)
sage: P.show()

>>> from sage.all import *
>>> C = graphs.CubeGraph(Integer(8))
>>> P = C.graphplot(vertex_labels=False, vertex_size=Integer(0),
...                 graph_border=True)
>>> P.show()

C = graphs.CubeGraph(8)
P = C.graphplot(vertex_labels=False, vertex_size=0,
                graph_border=True)
P.show()
../../_images/graph_plot-5.svg 
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u, v, l in G.edges(sort=True):
....:     G.set_edge_label(u, v, f'({u},{v})')
sage: G.graphplot(edge_labels=True).show()

>>> from sage.all import *
>>> G = graphs.HeawoodGraph().copy(sparse=True)
>>> for u, v, l in G.edges(sort=True):
...     G.set_edge_label(u, v, f'({u},{v})')
>>> G.graphplot(edge_labels=True).show()

G = graphs.HeawoodGraph().copy(sparse=True)
for u, v, l in G.edges(sort=True):
    G.set_edge_label(u, v, f'({u},{v})')
G.graphplot(edge_labels=True).show()
../../_images/graph_plot-6.svg

The options for plotting also work with directed graphs:

sage: D = DiGraph({
....:     0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4],
....:     4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9],
....:     9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13],
....:     13: [14], 14: [15], 15: [16], 16: [17], 17: [18],
....:     18: [19], 19: []})
sage: for u, v, l in D.edges(sort=True):
....:     D.set_edge_label(u, v, f'({u},{v})')
sage: D.graphplot(edge_labels=True, layout='circular').show()

>>> from sage.all import *
>>> D = DiGraph({
...     Integer(0): [Integer(1), Integer(10), Integer(19)], Integer(1): [Integer(8), Integer(2)], Integer(2): [Integer(3), Integer(6)], Integer(3): [Integer(19), Integer(4)],
...     Integer(4): [Integer(17), Integer(5)], Integer(5): [Integer(6), Integer(15)], Integer(6): [Integer(7)], Integer(7): [Integer(8), Integer(14)], Integer(8): [Integer(9)],
...     Integer(9): [Integer(10), Integer(13)], Integer(10): [Integer(11)], Integer(11): [Integer(12), Integer(18)], Integer(12): [Integer(16), Integer(13)],
...     Integer(13): [Integer(14)], Integer(14): [Integer(15)], Integer(15): [Integer(16)], Integer(16): [Integer(17)], Integer(17): [Integer(18)],
...     Integer(18): [Integer(19)], Integer(19): []})
>>> for u, v, l in D.edges(sort=True):
...     D.set_edge_label(u, v, f'({u},{v})')
>>> D.graphplot(edge_labels=True, layout='circular').show()

D = DiGraph({
    0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4],
    4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9],
    9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13],
    13: [14], 14: [15], 15: [16], 16: [17], 17: [18],
    18: [19], 19: []})
for u, v, l in D.edges(sort=True):
    D.set_edge_label(u, v, f'({u},{v})')
D.graphplot(edge_labels=True, layout='circular').show()
../../_images/graph_plot-7.svg

This example shows off the coloring of edges:

sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
....:     edge_colors[R[i]] = []
sage: for u, v, l in C.edges(sort=True):
....:     for i in range(5):
....:         if u[i] != v[i]:
....:             edge_colors[R[i]].append((u, v, l))
sage: C.graphplot(vertex_labels=False, vertex_size=0,
....:             edge_colors=edge_colors).show()

>>> from sage.all import *
>>> from sage.plot.colors import rainbow
>>> C = graphs.CubeGraph(Integer(5))
>>> R = rainbow(Integer(5))
>>> edge_colors = {}
>>> for i in range(Integer(5)):
...     edge_colors[R[i]] = []
>>> for u, v, l in C.edges(sort=True):
...     for i in range(Integer(5)):
...         if u[i] != v[i]:
...             edge_colors[R[i]].append((u, v, l))
>>> C.graphplot(vertex_labels=False, vertex_size=Integer(0),
...             edge_colors=edge_colors).show()

from sage.plot.colors import rainbow
C = graphs.CubeGraph(5)
R = rainbow(5)
edge_colors = {}
for i in range(5):
    edge_colors[R[i]] = []
for u, v, l in C.edges(sort=True):
    for i in range(5):
        if u[i] != v[i]:
            edge_colors[R[i]].append((u, v, l))
C.graphplot(vertex_labels=False, vertex_size=0,
            edge_colors=edge_colors).show()
../../_images/graph_plot-8.svg

With the partition option, we can separate out same-color groups of vertices:

sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6, 5, 15, 14, 7], [16, 13, 8, 2, 4],
....:       [12, 17, 9, 3, 1], [0, 19, 18, 10, 11]]
sage: D.show(partition=Pi)

>>> from sage.all import *
>>> D = graphs.DodecahedralGraph()
>>> Pi = [[Integer(6), Integer(5), Integer(15), Integer(14), Integer(7)], [Integer(16), Integer(13), Integer(8), Integer(2), Integer(4)],
...       [Integer(12), Integer(17), Integer(9), Integer(3), Integer(1)], [Integer(0), Integer(19), Integer(18), Integer(10), Integer(11)]]
>>> D.show(partition=Pi)

D = graphs.DodecahedralGraph()
Pi = [[6, 5, 15, 14, 7], [16, 13, 8, 2, 4],
      [12, 17, 9, 3, 1], [0, 19, 18, 10, 11]]
D.show(partition=Pi)
../../_images/graph_plot-9.svg

Loops are also plotted correctly:

sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()

>>> from sage.all import *
>>> G = graphs.PetersenGraph()
>>> G.allow_loops(True)
>>> G.add_edge(Integer(0),Integer(0))
>>> G.show()

G = graphs.PetersenGraph()
G.allow_loops(True)
G.add_edge(0,0)
G.show()
../../_images/graph_plot-10.svg 
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0, 1, 0): [(0, 1, None), (1, 2, None)],
....:                     (0, 0, 0): [(2, 3, None)]})

>>> from sage.all import *
>>> D = DiGraph({Integer(0):[Integer(0),Integer(1)], Integer(1):[Integer(2)], Integer(2):[Integer(3)]}, loops=True)
>>> D.show()
>>> D.show(edge_colors={(Integer(0), Integer(1), Integer(0)): [(Integer(0), Integer(1), None), (Integer(1), Integer(2), None)],
...                     (Integer(0), Integer(0), Integer(0)): [(Integer(2), Integer(3), None)]})

D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
D.show()
D.show(edge_colors={(0, 1, 0): [(0, 1, None), (1, 2, None)],
                    (0, 0, 0): [(2, 3, None)]})
../../_images/graph_plot-11.svg

More options:

sage: pos = {0: [0.0, 1.5], 1: [-0.8, 0.3], 2: [-0.6, -0.8],
....:        3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0: [1], 1: [2], 2: [3], 3: [4], 4: [0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
Graphics object consisting of 11 graphics primitives

>>> from sage.all import *
>>> pos = {Integer(0): [RealNumber('0.0'), RealNumber('1.5')], Integer(1): [-RealNumber('0.8'), RealNumber('0.3')], Integer(2): [-RealNumber('0.6'), -RealNumber('0.8')],
...        Integer(3):[RealNumber('0.6'), -RealNumber('0.8')], Integer(4):[RealNumber('0.8'), RealNumber('0.3')]}
>>> g = Graph({Integer(0): [Integer(1)], Integer(1): [Integer(2)], Integer(2): [Integer(3)], Integer(3): [Integer(4)], Integer(4): [Integer(0)]})
>>> g.graphplot(pos=pos, layout='spring', iterations=Integer(0)).plot()
Graphics object consisting of 11 graphics primitives

pos = {0: [0.0, 1.5], 1: [-0.8, 0.3], 2: [-0.6, -0.8],
       3:[0.6, -0.8], 4:[0.8, 0.3]}
g = Graph({0: [1], 1: [2], 2: [3], 3: [4], 4: [0]})
g.graphplot(pos=pos, layout='spring', iterations=0).plot()
../../_images/graph_plot-12.svg 
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False

>>> from sage.all import *
>>> G = Graph()
>>> P = G.graphplot().plot()
>>> P.axes()
False
>>> G = DiGraph()
>>> P = G.graphplot().plot()
>>> P.axes()
False

G = Graph()
P = G.graphplot().plot()
P.axes()
G = DiGraph()
P = G.graphplot().plot()
P.axes()

We can plot multiple graphs:

sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0: [0], 1: [4, 5, 1],
....:                      2: [2], 3: [3, 6]}
....:            ).plot()
Graphics object consisting of 14 graphics primitives

>>> from sage.all import *
>>> T = list(graphs.trees(Integer(7)))
>>> t = T[Integer(3)]
>>> t.graphplot(heights={Integer(0): [Integer(0)], Integer(1): [Integer(4), Integer(5), Integer(1)],
...                      Integer(2): [Integer(2)], Integer(3): [Integer(3), Integer(6)]}
...            ).plot()
Graphics object consisting of 14 graphics primitives

T = list(graphs.trees(7))
t = T[3]
t.graphplot(heights={0: [0], 1: [4, 5, 1],
                     2: [2], 3: [3, 6]}
           ).plot()
../../_images/graph_plot-13.svg 
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0: [0], 1: [4, 5, 1],
....:                      2: [2], 3: [3, 6]}
....:            ).plot()
Graphics object consisting of 14 graphics primitives

>>> from sage.all import *
>>> T = list(graphs.trees(Integer(7)))
>>> t = T[Integer(3)]
>>> t.graphplot(heights={Integer(0): [Integer(0)], Integer(1): [Integer(4), Integer(5), Integer(1)],
...                      Integer(2): [Integer(2)], Integer(3): [Integer(3), Integer(6)]}
...            ).plot()
Graphics object consisting of 14 graphics primitives

T = list(graphs.trees(7))
t = T[3]
t.graphplot(heights={0: [0], 1: [4, 5, 1],
                     2: [2], 3: [3, 6]}
           ).plot()
../../_images/graph_plot-14.svg 
sage: t.set_edge_label(0, 1, -7)
sage: t.set_edge_label(0, 5, 3)
sage: t.set_edge_label(0, 5, 99)
sage: t.set_edge_label(1, 2, 1000)
sage: t.set_edge_label(3, 2, 'spam')
sage: t.set_edge_label(2, 6, 3/2)
sage: t.set_edge_label(0, 4, 66)
sage: t.graphplot(heights={0: [0], 1: [4, 5, 1],
....:                      2: [2], 3: [3, 6]},
....:             edge_labels=True
....:            ).plot()
Graphics object consisting of 20 graphics primitives

>>> from sage.all import *
>>> t.set_edge_label(Integer(0), Integer(1), -Integer(7))
>>> t.set_edge_label(Integer(0), Integer(5), Integer(3))
>>> t.set_edge_label(Integer(0), Integer(5), Integer(99))
>>> t.set_edge_label(Integer(1), Integer(2), Integer(1000))
>>> t.set_edge_label(Integer(3), Integer(2), 'spam')
>>> t.set_edge_label(Integer(2), Integer(6), Integer(3)/Integer(2))
>>> t.set_edge_label(Integer(0), Integer(4), Integer(66))
>>> t.graphplot(heights={Integer(0): [Integer(0)], Integer(1): [Integer(4), Integer(5), Integer(1)],
...                      Integer(2): [Integer(2)], Integer(3): [Integer(3), Integer(6)]},
...             edge_labels=True
...            ).plot()
Graphics object consisting of 20 graphics primitives

t.set_edge_label(0, 1, -7)
t.set_edge_label(0, 5, 3)
t.set_edge_label(0, 5, 99)
t.set_edge_label(1, 2, 1000)
t.set_edge_label(3, 2, 'spam')
t.set_edge_label(2, 6, 3/2)
t.set_edge_label(0, 4, 66)
t.graphplot(heights={0: [0], 1: [4, 5, 1],
                     2: [2], 3: [3, 6]},
            edge_labels=True
           ).plot()
../../_images/graph_plot-15.svg 
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()

>>> from sage.all import *
>>> T = list(graphs.trees(Integer(7)))
>>> t = T[Integer(3)]
>>> t.graphplot(layout='tree').show()

T = list(graphs.trees(7))
t = T[3]
t.graphplot(layout='tree').show()
../../_images/graph_plot-16.svg

The tree layout is also useful:

sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0,
....:             tree_orientation="up"
....:            ).show()

>>> from sage.all import *
>>> t = DiGraph('JCC???@A??GO??CO??GO??')
>>> t.graphplot(layout='tree', tree_root=Integer(0),
...             tree_orientation="up"
...            ).show()

t = DiGraph('JCC???@A??GO??CO??GO??')
t.graphplot(layout='tree', tree_root=0,
            tree_orientation="up"
           ).show()
../../_images/graph_plot-17.svg

More examples:

sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()

>>> from sage.all import *
>>> D = DiGraph({Integer(0):[Integer(1),Integer(2),Integer(3)], Integer(2):[Integer(1),Integer(4)], Integer(3):[Integer(0)]})
>>> D.graphplot().show()

D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
D.graphplot().show()
../../_images/graph_plot-18.svg 
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
....:   D.add_edge((i, i + 1, 'a'))
....:   D.add_edge((i, i - 1, 'b'))
sage: D.graphplot(edge_labels=True,
....:             edge_colors=D._color_by_label()
....:            ).plot()
Graphics object consisting of 34 graphics primitives

>>> from sage.all import *
>>> D = DiGraph(multiedges=True, sparse=True)
>>> for i in range(Integer(5)):
...   D.add_edge((i, i + Integer(1), 'a'))
...   D.add_edge((i, i - Integer(1), 'b'))
>>> D.graphplot(edge_labels=True,
...             edge_colors=D._color_by_label()
...            ).plot()
Graphics object consisting of 34 graphics primitives

D = DiGraph(multiedges=True, sparse=True)
for i in range(5):
  D.add_edge((i, i + 1, 'a'))
  D.add_edge((i, i - 1, 'b'))
D.graphplot(edge_labels=True,
            edge_colors=D._color_by_label()
           ).plot()
../../_images/graph_plot-19.svg 
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
....:              (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
....:              (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
sage: g.graphplot(edge_labels=True,
....:             color_by_label=True,
....:             edge_style='dashed'
....:            ).plot()
Graphics object consisting of 22 graphics primitives

>>> from sage.all import *
>>> g = Graph({}, loops=True, multiedges=True, sparse=True)
>>> g.add_edges([(Integer(0), Integer(0), 'a'), (Integer(0), Integer(0), 'b'), (Integer(0), Integer(1), 'c'),
...              (Integer(0), Integer(1), 'd'), (Integer(0), Integer(1), 'e'), (Integer(0), Integer(1), 'f'),
...              (Integer(0), Integer(1), 'f'), (Integer(2), Integer(1), 'g'), (Integer(2), Integer(2), 'h')])
>>> g.graphplot(edge_labels=True,
...             color_by_label=True,
...             edge_style='dashed'
...            ).plot()
Graphics object consisting of 22 graphics primitives

g = Graph({}, loops=True, multiedges=True, sparse=True)
g.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
             (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
             (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
g.graphplot(edge_labels=True,
            color_by_label=True,
            edge_style='dashed'
           ).plot()
../../_images/graph_plot-20.svg

The edge_style option may be provided in the short format too:

sage: g.graphplot(edge_labels=True,
....:             color_by_label=True,
....:             edge_style='--'
....:            ).plot()
Graphics object consisting of 22 graphics primitives

>>> from sage.all import *
>>> g.graphplot(edge_labels=True,
...             color_by_label=True,
...             edge_style='--'
...            ).plot()
Graphics object consisting of 22 graphics primitives

g.graphplot(edge_labels=True,
            color_by_label=True,
            edge_style='--'
           ).plot()
set_edges(**edge_options)[source]

Set edge plotting parameters for the GraphPlot object.

This function is called by the constructor but can also be called to update the edge options of an existing GraphPlot object. Note that the changes are cumulative.

EXAMPLES:

sage: g = Graph(loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
....:              (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
....:              (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
sage: GP = g.graphplot(vertex_size=100, edge_labels=True,
....:                  color_by_label=True, edge_style='dashed')
sage: GP.set_edges(edge_style='solid')
sage: GP.plot()
Graphics object consisting of 22 graphics primitives

>>> from sage.all import *
>>> g = Graph(loops=True, multiedges=True, sparse=True)
>>> g.add_edges([(Integer(0), Integer(0), 'a'), (Integer(0), Integer(0), 'b'), (Integer(0), Integer(1), 'c'),
...              (Integer(0), Integer(1), 'd'), (Integer(0), Integer(1), 'e'), (Integer(0), Integer(1), 'f'),
...              (Integer(0), Integer(1), 'f'), (Integer(2), Integer(1), 'g'), (Integer(2), Integer(2), 'h')])
>>> GP = g.graphplot(vertex_size=Integer(100), edge_labels=True,
...                  color_by_label=True, edge_style='dashed')
>>> GP.set_edges(edge_style='solid')
>>> GP.plot()
Graphics object consisting of 22 graphics primitives

g = Graph(loops=True, multiedges=True, sparse=True)
g.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
             (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
             (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
GP = g.graphplot(vertex_size=100, edge_labels=True,
                 color_by_label=True, edge_style='dashed')
GP.set_edges(edge_style='solid')
GP.plot()
../../_images/graph_plot-21.svg 
sage: GP.set_edges(edge_color='black')
sage: GP.plot()
Graphics object consisting of 22 graphics primitives

>>> from sage.all import *
>>> GP.set_edges(edge_color='black')
>>> GP.plot()
Graphics object consisting of 22 graphics primitives

GP.set_edges(edge_color='black')
GP.plot()
../../_images/graph_plot-22.svg 
sage: d = DiGraph(loops=True, multiedges=True, sparse=True)
sage: d.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
....:              (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
....:              (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
sage: GP = d.graphplot(vertex_size=100, edge_labels=True,
....:                  color_by_label=True, edge_style='dashed')
sage: GP.set_edges(edge_style='solid')
sage: GP.plot()
Graphics object consisting of 24 graphics primitives

>>> from sage.all import *
>>> d = DiGraph(loops=True, multiedges=True, sparse=True)
>>> d.add_edges([(Integer(0), Integer(0), 'a'), (Integer(0), Integer(0), 'b'), (Integer(0), Integer(1), 'c'),
...              (Integer(0), Integer(1), 'd'), (Integer(0), Integer(1), 'e'), (Integer(0), Integer(1), 'f'),
...              (Integer(0), Integer(1), 'f'), (Integer(2), Integer(1), 'g'), (Integer(2), Integer(2), 'h')])
>>> GP = d.graphplot(vertex_size=Integer(100), edge_labels=True,
...                  color_by_label=True, edge_style='dashed')
>>> GP.set_edges(edge_style='solid')
>>> GP.plot()
Graphics object consisting of 24 graphics primitives

d = DiGraph(loops=True, multiedges=True, sparse=True)
d.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
             (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
             (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
GP = d.graphplot(vertex_size=100, edge_labels=True,
                 color_by_label=True, edge_style='dashed')
GP.set_edges(edge_style='solid')
GP.plot()
../../_images/graph_plot-23.svg 
sage: GP.set_edges(edge_color='black')
sage: GP.plot()
Graphics object consisting of 24 graphics primitives

>>> from sage.all import *
>>> GP.set_edges(edge_color='black')
>>> GP.plot()
Graphics object consisting of 24 graphics primitives

GP.set_edges(edge_color='black')
GP.plot()
../../_images/graph_plot-24.svg
set_pos()[source]

Set the position plotting parameters for this GraphPlot.

EXAMPLES:

This function is called implicitly by the code below:

sage: g = Graph({0: [1, 2], 2: [3], 4: [0, 1]})
sage: g.graphplot(save_pos=True, layout='circular')  # indirect doctest
GraphPlot object for Graph on 5 vertices

>>> from sage.all import *
>>> g = Graph({Integer(0): [Integer(1), Integer(2)], Integer(2): [Integer(3)], Integer(4): [Integer(0), Integer(1)]})
>>> g.graphplot(save_pos=True, layout='circular')  # indirect doctest
GraphPlot object for Graph on 5 vertices

g = Graph({0: [1, 2], 2: [3], 4: [0, 1]})
g.graphplot(save_pos=True, layout='circular')  # indirect doctest

The following illustrates the format of a position dictionary, but due to numerical noise we do not check the values themselves:

sage: g.get_pos()
{0: (0.0, 1.0),
 1: (-0.951..., 0.309...),
 2: (-0.587..., -0.809...),
 3: (0.587..., -0.809...),
 4: (0.951..., 0.309...)}

>>> from sage.all import *
>>> g.get_pos()
{0: (0.0, 1.0),
 1: (-0.951..., 0.309...),
 2: (-0.587..., -0.809...),
 3: (0.587..., -0.809...),
 4: (0.951..., 0.309...)}

g.get_pos()

sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.plot(heights={0: [0], 1: [4, 5, 1], 2: [2], 3: [3, 6]})
Graphics object consisting of 14 graphics primitives

>>> from sage.all import *
>>> T = list(graphs.trees(Integer(7)))
>>> t = T[Integer(3)]
>>> t.plot(heights={Integer(0): [Integer(0)], Integer(1): [Integer(4), Integer(5), Integer(1)], Integer(2): [Integer(2)], Integer(3): [Integer(3), Integer(6)]})
Graphics object consisting of 14 graphics primitives

T = list(graphs.trees(7))
t = T[3]
t.plot(heights={0: [0], 1: [4, 5, 1], 2: [2], 3: [3, 6]})
../../_images/graph_plot-25.svg
set_vertices(**vertex_options)[source]

Set the vertex plotting parameters for this GraphPlot.

This function is called by the constructor but can also be called to make updates to the vertex options of an existing GraphPlot object. Note that the changes are cumulative.

EXAMPLES:

sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
....:              (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
....:              (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
sage: GP = g.graphplot(vertex_size=100, edge_labels=True,
....:                  color_by_label=True, edge_style='dashed')
sage: GP.set_vertices(talk=True)
sage: GP.plot()
Graphics object consisting of 22 graphics primitives
sage: GP.set_vertices(vertex_color='green', vertex_shape='^')
sage: GP.plot()
Graphics object consisting of 22 graphics primitives

>>> from sage.all import *
>>> g = Graph({}, loops=True, multiedges=True, sparse=True)
>>> g.add_edges([(Integer(0), Integer(0), 'a'), (Integer(0), Integer(0), 'b'), (Integer(0), Integer(1), 'c'),
...              (Integer(0), Integer(1), 'd'), (Integer(0), Integer(1), 'e'), (Integer(0), Integer(1), 'f'),
...              (Integer(0), Integer(1), 'f'), (Integer(2), Integer(1), 'g'), (Integer(2), Integer(2), 'h')])
>>> GP = g.graphplot(vertex_size=Integer(100), edge_labels=True,
...                  color_by_label=True, edge_style='dashed')
>>> GP.set_vertices(talk=True)
>>> GP.plot()
Graphics object consisting of 22 graphics primitives
>>> GP.set_vertices(vertex_color='green', vertex_shape='^')
>>> GP.plot()
Graphics object consisting of 22 graphics primitives

g = Graph({}, loops=True, multiedges=True, sparse=True)
g.add_edges([(0, 0, 'a'), (0, 0, 'b'), (0, 1, 'c'),
             (0, 1, 'd'), (0, 1, 'e'), (0, 1, 'f'),
             (0, 1, 'f'), (2, 1, 'g'), (2, 2, 'h')])
GP = g.graphplot(vertex_size=100, edge_labels=True,
                 color_by_label=True, edge_style='dashed')
GP.set_vertices(talk=True)
GP.plot()
GP.set_vertices(vertex_color='green', vertex_shape='^')
GP.plot()
../../_images/graph_plot-26.svg
../../_images/graph_plot-27.svg

Vertex labels are flexible:

sage: g = graphs.PathGraph(4)
sage: g.plot(vertex_labels=False)
Graphics object consisting of 4 graphics primitives

>>> from sage.all import *
>>> g = graphs.PathGraph(Integer(4))
>>> g.plot(vertex_labels=False)
Graphics object consisting of 4 graphics primitives

g = graphs.PathGraph(4)
g.plot(vertex_labels=False)
../../_images/graph_plot-28.svg 
sage: g = graphs.PathGraph(4)
sage: g.plot(vertex_labels=True)
Graphics object consisting of 8 graphics primitives

>>> from sage.all import *
>>> g = graphs.PathGraph(Integer(4))
>>> g.plot(vertex_labels=True)
Graphics object consisting of 8 graphics primitives

g = graphs.PathGraph(4)
g.plot(vertex_labels=True)
../../_images/graph_plot-29.svg 
sage: g = graphs.PathGraph(4)
sage: g.plot(vertex_labels=dict(zip(g, ['+', '-', '/', '*'])))
Graphics object consisting of 8 graphics primitives

>>> from sage.all import *
>>> g = graphs.PathGraph(Integer(4))
>>> g.plot(vertex_labels=dict(zip(g, ['+', '-', '/', '*'])))
Graphics object consisting of 8 graphics primitives

g = graphs.PathGraph(4)
g.plot(vertex_labels=dict(zip(g, ['+', '-', '/', '*'])))
../../_images/graph_plot-30.svg 
sage: g = graphs.PathGraph(4)
sage: g.plot(vertex_labels=lambda x: str(x % 2))
Graphics object consisting of 8 graphics primitives

>>> from sage.all import *
>>> g = graphs.PathGraph(Integer(4))
>>> g.plot(vertex_labels=lambda x: str(x % Integer(2)))
Graphics object consisting of 8 graphics primitives

g = graphs.PathGraph(4)
g.plot(vertex_labels=lambda x: str(x % 2))
../../_images/graph_plot-31.svg
show(**kwds)[source]

Show the (di)graph associated with this GraphPlot object.

INPUT:

This method accepts all parameters of sage.plot.graphics.Graphics.show().

Note

EXAMPLES:

sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0,
....:                 graph_border=True)
sage: P.show()

>>> from sage.all import *
>>> C = graphs.CubeGraph(Integer(8))
>>> P = C.graphplot(vertex_labels=False, vertex_size=Integer(0),
...                 graph_border=True)
>>> P.show()

C = graphs.CubeGraph(8)
P = C.graphplot(vertex_labels=False, vertex_size=0,
                graph_border=True)
P.show()
../../_images/graph_plot-32.svg