Lists of graphs

AUTHORS:

  • Robert L. Miller (2007-02-10): initial version

  • Emily A. Kirkman (2007-02-13): added show functions (to_graphics_array and show_graphs)

sage.graphs.graph_list.from_graph6(data)[source]

Return a list of Sage Graphs, given a list of graph6 data.

INPUT:

  • data – can be a string, a list of strings, or a file stream

EXAMPLES:

sage: l = ['N@@?N@UGAGG?gGlKCMO', 'XsGGWOW?CC?C@HQKHqOjYKC_uHWGX?P?~TqIKA`OA@SAOEcEA??']
sage: graphs_list.from_graph6(l)
[Graph on 15 vertices, Graph on 25 vertices]

>>> from sage.all import *
>>> l = ['N@@?N@UGAGG?gGlKCMO', 'XsGGWOW?CC?C@HQKHqOjYKC_uHWGX?P?~TqIKA`OA@SAOEcEA??']
>>> graphs_list.from_graph6(l)
[Graph on 15 vertices, Graph on 25 vertices]
sage.graphs.graph_list.from_sparse6(data)[source]

Return a list of Sage Graphs, given a list of sparse6 data.

INPUT:

  • data – can be a string, a list of strings, or a file stream

EXAMPLES:

sage: g1 = ':P_`cBaC_ACd`C_@BC`ABDHaEH_@BF_@CHIK_@BCEHKL_BIKM_BFGHI'
sage: g2 = ':f`??KO?B_OOSCGE_?OWONDBO?GOJBDO?_SSJdApcOIG`?og_UKEbg?_SKF'
sage: g2 += 'q@[CCBA`p?oYMFp@gw]Qaa@xEMHDb@hMCBCbQ@ECHEcAKKQKFPOwo[PIDQ'
sage: g2 += '{KIHEcQPOkVKEW_WMNKqPWwcRKOOWSKIGCqhWt??___WMJFCahWzEBa`xO'
sage: g2 += 'u[MpPPKqYNoOOOKHHDBPs|??__gWMKEcAHKgTLErqA?A@a@G{kVLErs?GD'
sage: g2 += 'BA@XCs\NggWSOJIDbHh@?A@aF'
sage: graphs_list.from_sparse6([g1, g2])
[Looped multi-graph on 17 vertices, Looped multi-graph on 39 vertices]

>>> from sage.all import *
>>> g1 = ':P_`cBaC_ACd`C_@BC`ABDHaEH_@BF_@CHIK_@BCEHKL_BIKM_BFGHI'
>>> g2 = ':f`??KO?B_OOSCGE_?OWONDBO?GOJBDO?_SSJdApcOIG`?og_UKEbg?_SKF'
>>> g2 += 'q@[CCBA`p?oYMFp@gw]Qaa@xEMHDb@hMCBCbQ@ECHEcAKKQKFPOwo[PIDQ'
>>> g2 += '{KIHEcQPOkVKEW_WMNKqPWwcRKOOWSKIGCqhWt??___WMJFCahWzEBa`xO'
>>> g2 += 'u[MpPPKqYNoOOOKHHDBPs|??__gWMKEcAHKgTLErqA?A@a@G{kVLErs?GD'
>>> g2 += 'BA@XCs\NggWSOJIDbHh@?A@aF'
>>> graphs_list.from_sparse6([g1, g2])
[Looped multi-graph on 17 vertices, Looped multi-graph on 39 vertices]
sage.graphs.graph_list.from_whatever(data)[source]

Return a list of Sage Graphs, given a list of whatever kind of data.

INPUT:

  • data – can be a string, a list/iterable of strings, or a readable file-like object

EXAMPLES:

sage: l = ['N@@?N@UGAGG?gGlKCMO', ':P_`cBaC_ACd`C_@BC`ABDHaEH_@BF_@CHIK_@BCEHKL_BIKM_BFGHI']
sage: graphs_list.from_whatever(l)
[Graph on 15 vertices, Looped multi-graph on 17 vertices]
sage: graphs_list.from_whatever('\n'.join(l))
[Graph on 15 vertices, Looped multi-graph on 17 vertices]

>>> from sage.all import *
>>> l = ['N@@?N@UGAGG?gGlKCMO', ':P_`cBaC_ACd`C_@BC`ABDHaEH_@BF_@CHIK_@BCEHKL_BIKM_BFGHI']
>>> graphs_list.from_whatever(l)
[Graph on 15 vertices, Looped multi-graph on 17 vertices]
>>> graphs_list.from_whatever('\n'.join(l))
[Graph on 15 vertices, Looped multi-graph on 17 vertices]

This example happens to be a mix a sparse and non-sparse graphs, so we don’t explicitly put a .g6 or .s6 extension, which implies just one or the other:

sage: filename = tmp_filename()
sage: with open(filename, 'w') as fobj:
....:     _ = fobj.write('\n'.join(l))
sage: with open(filename) as fobj:
....:     graphs_list.from_whatever(fobj)
[Graph on 15 vertices, Looped multi-graph on 17 vertices]

>>> from sage.all import *
>>> filename = tmp_filename()
>>> with open(filename, 'w') as fobj:
...     _ = fobj.write('\n'.join(l))
>>> with open(filename) as fobj:
...     graphs_list.from_whatever(fobj)
[Graph on 15 vertices, Looped multi-graph on 17 vertices]
sage.graphs.graph_list.show_graphs(graph_list, **kwds)[source]

Show a maximum of 20 graphs from graph_list in a sage graphics array.

If more than 20 graphs are given in the list argument, then it will display one graphics array after another with each containing at most 20 graphs.

Note that to save the image output from the notebook, you must save each graphics array individually. (There will be a small space between graphics arrays).

INPUT:

  • graph_list – a Python list of Sage Graphs

GRAPH PLOTTING: Defaults to circular layout for graphs. This allows for a nicer display in a small area and takes much less time to compute than the spring-layout algorithm for many graphs.

EXAMPLES: Create a list of graphs:

sage: glist = []
sage: glist.append(graphs.CompleteGraph(6))
sage: glist.append(graphs.CompleteBipartiteGraph(4, 5))
sage: glist.append(graphs.BarbellGraph(7, 4))
sage: glist.append(graphs.CycleGraph(15))
sage: glist.append(graphs.DiamondGraph())
sage: glist.append(graphs.GemGraph())
sage: glist.append(graphs.DartGraph())
sage: glist.append(graphs.ForkGraph())
sage: glist.append(graphs.HouseGraph())
sage: glist.append(graphs.HouseXGraph())
sage: glist.append(graphs.KrackhardtKiteGraph())
sage: glist.append(graphs.LadderGraph(5))
sage: glist.append(graphs.LollipopGraph(5, 6))
sage: glist.append(graphs.PathGraph(15))
sage: glist.append(graphs.PetersenGraph())
sage: glist.append(graphs.StarGraph(17))
sage: glist.append(graphs.WheelGraph(9))

>>> from sage.all import *
>>> glist = []
>>> glist.append(graphs.CompleteGraph(Integer(6)))
>>> glist.append(graphs.CompleteBipartiteGraph(Integer(4), Integer(5)))
>>> glist.append(graphs.BarbellGraph(Integer(7), Integer(4)))
>>> glist.append(graphs.CycleGraph(Integer(15)))
>>> glist.append(graphs.DiamondGraph())
>>> glist.append(graphs.GemGraph())
>>> glist.append(graphs.DartGraph())
>>> glist.append(graphs.ForkGraph())
>>> glist.append(graphs.HouseGraph())
>>> glist.append(graphs.HouseXGraph())
>>> glist.append(graphs.KrackhardtKiteGraph())
>>> glist.append(graphs.LadderGraph(Integer(5)))
>>> glist.append(graphs.LollipopGraph(Integer(5), Integer(6)))
>>> glist.append(graphs.PathGraph(Integer(15)))
>>> glist.append(graphs.PetersenGraph())
>>> glist.append(graphs.StarGraph(Integer(17)))
>>> glist.append(graphs.WheelGraph(Integer(9)))

Check that length is <= 20:

sage: len(glist)
17

>>> from sage.all import *
>>> len(glist)
17

Show the graphs in a graphics array:

sage: graphs_list.show_graphs(glist)                                            # needs sage.plot

>>> from sage.all import *
>>> graphs_list.show_graphs(glist)                                            # needs sage.plot

Example where more than one graphics array is used:

sage: gq = GraphQuery(display_cols=['graph6'], num_vertices=5)
sage: g = gq.get_graphs_list()
sage: len(g)
34
sage: graphs_list.show_graphs(g)                                                # needs sage.plot

>>> from sage.all import *
>>> gq = GraphQuery(display_cols=['graph6'], num_vertices=Integer(5))
>>> g = gq.get_graphs_list()
>>> len(g)
34
>>> graphs_list.show_graphs(g)                                                # needs sage.plot

See the .plot() or .show() documentation for an individual graph for options, all of which are available from to_graphics_array():

sage: glist = []
sage: for _ in range(10):                                                       # needs networkx
....:     glist.append(graphs.RandomLobster(41, .3, .4))
sage: graphs_list.show_graphs(glist, layout='spring', vertex_size=20)           # needs sage.plot

>>> from sage.all import *
>>> glist = []
>>> for _ in range(Integer(10)):                                                       # needs networkx
...     glist.append(graphs.RandomLobster(Integer(41), RealNumber('.3'), RealNumber('.4')))
>>> graphs_list.show_graphs(glist, layout='spring', vertex_size=Integer(20))           # needs sage.plot
sage.graphs.graph_list.to_graph6(graphs, file=None, output_list=False)[source]

Convert a list of Sage graphs to a single string of graph6 graphs.

If file is specified, then the string will be written quietly to the file. If output_list is True, then a list of strings will be returned, one string per graph.

INPUT:

  • graphs – a Python list of Sage Graphs

  • file – (optional) a file stream to write to (must be in ‘w’ mode)

  • output_list – boolean (default: False); whether to return a string (when set to True) or a list of strings. This parameter is ignored if file gets specified

EXAMPLES:

sage: l = [graphs.DodecahedralGraph(), graphs.PetersenGraph()]
sage: graphs_list.to_graph6(l)
'ShCHGD@?K?_@?@?C_GGG@??cG?G?GK_?C\nIheA@GUAo\n'

>>> from sage.all import *
>>> l = [graphs.DodecahedralGraph(), graphs.PetersenGraph()]
>>> graphs_list.to_graph6(l)
'ShCHGD@?K?_@?@?C_GGG@??cG?G?GK_?C\nIheA@GUAo\n'
sage.graphs.graph_list.to_graphics_array(graph_list, **kwds)[source]

Draw all graphs in a graphics array.

INPUT:

  • graph_list – a Python list of Sage Graphs

GRAPH PLOTTING:

Defaults to circular layout for graphs. This allows for a nicer display in a small area and takes much less time to compute than the spring- layout algorithm for many graphs.

EXAMPLES:

sage: glist = []
sage: for i in range(999):
....:     glist.append(graphs.RandomGNP(6, .45))
sage: garray = graphs_list.to_graphics_array(glist)                             # needs sage.plot
sage: garray.nrows(), garray.ncols()                                            # needs sage.plot
(250, 4)

>>> from sage.all import *
>>> glist = []
>>> for i in range(Integer(999)):
...     glist.append(graphs.RandomGNP(Integer(6), RealNumber('.45')))
>>> garray = graphs_list.to_graphics_array(glist)                             # needs sage.plot
>>> garray.nrows(), garray.ncols()                                            # needs sage.plot
(250, 4)

See the .plot() or .show() documentation for an individual graph for options, all of which are available from to_graphics_array():

sage: glist = []
sage: for _ in range(10):                                                       # needs networkx
....:     glist.append(graphs.RandomLobster(41, .3, .4))
sage: graphs_list.to_graphics_array(glist, layout='spring', vertex_size=20)     # needs networkx sage.plot
Graphics Array of size 3 x 4

>>> from sage.all import *
>>> glist = []
>>> for _ in range(Integer(10)):                                                       # needs networkx
...     glist.append(graphs.RandomLobster(Integer(41), RealNumber('.3'), RealNumber('.4')))
>>> graphs_list.to_graphics_array(glist, layout='spring', vertex_size=Integer(20))     # needs networkx sage.plot
Graphics Array of size 3 x 4
sage.graphs.graph_list.to_sparse6(graphs, file=None, output_list=False)[source]

Convert a list of Sage graphs to a single string of sparse6 graphs.

If file is specified, then the string will be written quietly to the file. If output_list is True, then a list of strings will be returned, one string per graph.

INPUT:

  • graphs – a Python list of Sage Graphs

  • file – (optional) a file stream to write to (must be in ‘w’ mode)

  • output_list – boolean (default: False); whether to return a string (when set to True) or a list of strings. This parameter is ignored if file gets specified

EXAMPLES:

sage: l = [graphs.DodecahedralGraph(), graphs.PetersenGraph()]
sage: graphs_list.to_sparse6(l)
':S_`abcaDe`Fg_HijhKfLdMkNcOjP_BQ\n:I`ES@obGkqegW~\n'

>>> from sage.all import *
>>> l = [graphs.DodecahedralGraph(), graphs.PetersenGraph()]
>>> graphs_list.to_sparse6(l)
':S_`abcaDe`Fg_HijhKfLdMkNcOjP_BQ\n:I`ES@obGkqegW~\n'