A module for dealing with 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)

Returns 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.

EXAMPLE:

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]

sage.graphs.graph_list.from_sparse6(data)

Returns 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.

EXAMPLE:

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

sage.graphs.graph_list.from_whatever(data)

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

INPUT:

• data - can be a string, a list of strings, or a file stream, or whatever.

EXAMPLE:

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.graph_list.show_graphs(list, **kwds)

Shows a maximum of 20 graphs from 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 if 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:

• list - a 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.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))

Check that length is = 20:

sage: len(glist)
14

Show the graphs in a graphics array:

sage: graphs_list.show_graphs(glist)

Here’s an 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)

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

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

sage.graphs.graph_list.to_graph6(list, file=None, output_list=False)

Converts 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:

• list - a Python list of Sage Graphs
• file - (optional) a file stream to write to (must be in ‘w’ mode)
• output_list - False - output is a string True - output is a list of strings (ignored if file gets specified)

EXAMPLE:

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

sage.graphs.graph_list.to_graphics_arrays(list, **kwds)

Returns a list of Sage graphics arrays containing the graphs in list. The maximum number of graphs per array is 20 (5 rows of 4). Use this function if there are too many graphs for the show_graphs function. The graphics arrays will contain 20 graphs each except potentially the last graphics array in the list.

INPUT:

• list - a 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_arrays(glist)

Display the first graphics array in the list.

sage: garray[0].show()

Display the last graphics array in the list.

sage: garray[len(garray)-1].show()

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

sage: glist = []
sage: for _ in range(10):
...       glist.append(graphs.RandomLobster(41, .3, .4))
sage: w = graphs_list.to_graphics_arrays(glist, layout='spring', vertex_size=20)
sage: len(w)
1
sage: w[0]

sage.graphs.graph_list.to_sparse6(list, file=None, output_list=False)

Converts 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:

• list - a Python list of Sage Graphs
• file - (optional) a file stream to write to (must be in ‘w’ mode)
• output_list - False - output is a string True - output is a list of strings (ignored if file gets specified)

EXAMPLE:

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