Differences between revisions 12 and 18 (spanning 6 versions)

Emily Kirkman is working on this project. [http://sage.math.washington.edu:9001/graph Back to main wiki.]

The goal of the Graph Generators Class is to implement constructors for many common graphs, as well as thorough docstrings that can be used for reference. The graph generators will grow as the Graph Theory Project does. So please check back for additions and feel free to leave requests in the suggestions section.

We currently have 30 constructors of named graphs and basic structures. Most of these graphs are constructed with a preset dictionary of x-y coordinates of each node. This is advantageous for both style and time. (The default graph plotting in SAGE uses the spring-layout algorithm). SAGE graphs all have an associated graphics object, and examples of plotting options are shown on the graphs below.

As we implement algorithms into the Graph Theory Package, the constructors of known graphs would set their properties upon instantiation as well. For example, if someone created a very large complete bipartite graph and then asked if it is a bipartite graph (not currently implemented), then instead of running through an algorithm to check it, we could return a value set at instantiation. Further, this will improve the reference use of the docstrings as we would list the properties of each named graph.

Due to the volume of graphs now in the generators class, this wiki page is now intended to give status updates and serve as a gallery of graphs currently implemented. To see information on a specific graph, run SAGE or the SAGE [http://sage.math.washington.edu:8100 notebook]. For a list of graph constructors, type "graphs." and hit tab. For docstrings, type the graph name and one question mark (i.e.: "graphs.CubeGraph?") then shift + enter. For source code, do likewise with two question marks.

TableOfContents

Suggestions

Graphs I Plan to Add

Inherited from NetworkX

Bipartite Generators
Balanced tree
Dorogovstev golstev mendes graph
Grid (n-dim)
Chvatal
Desargues
Pappus
Sedgewick
Truncated cube
Truncated tetrahedron
Tutte
Also many more random generators and gens from degree sequence to sort through

Families of Graphs

Generalized Petersen graphs
Petersen Graph family
Trees (Directed – not simple. Maybe Balanced tree constructor and query isTree)
Cayley (Requires Edge Coloring)
Paley

Named Graphs

Brinkman
Clebsch
Icosahedron
Grötzsch graph
Tutte eight-cage
Szekeres snark
Thomassen graph
Johnson (maybe own class)
Turan

Gallery of Graph Generators in SAGE

Named Graphs

Flower Snark

sage: flower_snark = graphs.FlowerSnark()
sage: flower_snark.set_boundary([15,16,17,18,19])
sage: flower_snark.show(figsize=[4,4], graph_border=True)

attachment:flower.png

Frucht

sage: frucht = graphs.FruchtGraph()
sage: frucht.show(figsize=[4,4], graph_border=True)

attachment:frucht.png

Heawood

sage: heawood = graphs.HeawoodGraph()
sage: heawood.show(figsize=[4,4], graph_border=True)

attachment:heawood.png

Möbius Kantor

sage: moebius_kantor = graphs.MoebiusKantorGraph()
sage: moebius_kantor.show(figsize=[4,4], graph_border=True)

attachment:moebiuskantor.png

Petersen

sage: petersen = graphs.PetersenGraph()
sage: petersen.show(figsize=[4,4], graph_border=True)

attachment:petersen.png

Thomsen

sage: thomsen = graphs.ThomsenGraph()
sage: thomsen.show(figsize=[4,4], graph_border=True)

attachment:thomsen.png

Graph Families

Complete Bipartite Graphs

sage: comp_bip_list = []
sage: for i in range (2):
... for j in range (4):
...  comp_bip_list.append(graphs.CompleteBipartiteGraph(i+3,j+1))
...
sage: graphs_list.show_graphs(comp_bip_list)

attachment:compbip.png

Complete Graphs

sage: comp_list = []
sage: for i in range(13)[1:]:
... comp_list.append(graphs.CompleteGraph(i))
...
sage: graphs_list.show_graphs(comp_list)

attachment:complete.png

Cube Graphs

sage: cube_list = []
sage: for i in range(6)[2:]:
... cube_list.append(graphs.CubeGraph(i))
...
sage: graphs_list.show_graphs(cube_list)

attachment:cube.png

sage: bigger_cube = graphs.CubeGraph(8)
sage: bigger_cube.show(figsize=[8,8], node_size=20, vertex_labels=False, graph_border=True)

attachment:biggercube.png

Basic Structures

Barbell Graph

sage: barbell_list = []
sage: for i in range (4):
... for j in range (2):
...  barbell_list.append(graphs.BarbellGraph(i+3, j+2))
...
sage: graphs_list.show_graphs(barbell_list)

attachment:barbell.png

Bull Graph

sage: bull = graphs.BullGraph()
sage: bull.show(figsize=[4,4], graph_border=True)

attachment:bull.png

Circular Ladder Graph

sage: circ_ladder = graphs.CircularLadderGraph(9)
sage: circ_ladder.show(figsize=[4,4], graph_border=True)

attachment:circladder.png

Claw Graph

sage: claw = graphs.ClawGraph()
sage: claw.show(figsize=[4,4], graph_border=True)

attachment:claw.png

Cycle Graphs

sage: cycle = graphs.CycleGraph(17)
sage: cycle.show(figsize=[4,4], graph_border=True)

attachment:cycle.png

Diamond Graph

sage: diamond = graphs.DiamondGraph()
sage: diamond.show(figsize=[4,4], graph_border=True)

attachment:diamond.png

Dodecahedral Graph

sage: dodecahedral = graphs.DodecahedralGraph()
sage: dodecahedral.show(figsize=[4,4], vertex_labels=False, node_size=50, graph_border=True)

attachment:dodecahedral.png

Empty Graph

sage: empty = graphs.EmptyGraph()
sage: empty.show(figsize=[1,1], graph_border=True)

attachment:empty.png

Grid 2d Graph

sage: grid = graphs.Grid2dGraph(3,5)
sage: grid.show(figsize=[5,3])

attachment:grid.png

House Graph

sage: house = graphs.HouseGraph()
sage: house.show(figsize=[4,4], graph_border=True)

attachment:house.png

House X Graph

sage: houseX = graphs.HouseXGraph()
sage: houseX.show(figsize=[4,4], graph_border=True)

attachment:housex.png

Krackhardt Kite Graph

sage: krackhardt = graphs.KrackhardtKiteGraph()
sage: krackhardt.show(figsize=[4,4], graph_border=True)

attachment:krack.png

Ladder Graph

sage: ladder = graphs.LadderGraph(5)
sage: ladder.show(figsize=[4,4], graph_border=True)

attachment:ladder.png

Lollipop Graph

sage: lollipop_list = []
sage: for i in range (4):
... for j in range (2):
...  lollipop_list.append(graphs.LollipopGraph(i+3, j+2))
...
sage: graphs_list.show_graphs(lollipop_list)

attachment:lollipop.png

Octahedral Graph

sage: octahedral = graphs.OctahedralGraph()
sage: octahedral.show(figsize=[4,4], vertex_labels=False, node_size=50, graph_border=True)

attachment:octahedral.png

Path Graph

sage: path_line = graphs.PathGraph(5)
sage: path_circle = graphs.PathGraph(15)
sage: path_maze = graphs.PathGraph(45)
sage: path_list = [path_line, path_circle, path_maze]
sage: graphs_list.show_graphs(path_list)

attachment:path.png

Star Graph

sage: star_list = []
sage: for i in range (12)[4:]:
... star_list.append(graphs.StarGraph(i))
...
sage: graphs_list.show_graphs(star_list)

attachment:star.png

Tetrahedral Graph

sage: tetrahedral = graphs.TetrahedralGraph()
sage: tetrahedral.show(figsize=[4,4], graph_border=True)

attachment:tetrahedral.png

Wheel Graph

sage: wheel_list = []
sage: for i in range (12)[4:]:
... wheel_list.append(graphs.WheelGraph(i))
...
sage: graphs_list.show_graphs(wheel_list)

attachment:wheel.png

Random Generators

Random GNP

Use for dense graphs:

time
sage: (graphs.RandomGNP(16,.77)).show(figsize=[4,4], graph_border=True)

My results: CPU time: 0.74 s, Wall time: 0.73 s attachment:random.png

Random GNP Fast

Use for sparse graphs:

time
sage: (graphs.RandomGNPFast(16,.19)).show(figsize=[4,4], graph_border=True)

My results: CPU time: 0.63 s, Wall time: 0.62 s attachment:randomfast.png

-  ⇤ ← Revision 12 as of 2007-02-19 11:23:40 → 
  Size: 4035
  Editor: anonymous
  Comment:
+   ← Revision 18 as of 2007-03-01 11:03:30 → ⇥
  Size: 8428
  Editor: anonymous
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 1:
-Emily Kirkman is working on this project.

The goal of the Graph Generators Class is to implement constructors for many common graphs, as well as thorough docstrings that can be used for reference.  The graph generators will grow as the Graph Theory Project does.  So please check back for additions and feel free to leave requests in the suggestions section.  

We currently have 30 constructors of named graphs and basic structures.  Most of these graphs are constructed with a preset dictionary of x-y coordinates of each node.  This is advantageous for both style and time.  (The default graph plotting in SAGE using the spring-layout algorithm).  SAGE graphs all have an associated graphics object, and examples of plotting options are shown on the graphs below.
+Emily Kirkman is working on this project.  [http://sage.math.washington.edu:9001/graph Back to main wiki.]

The goal of the Graph Generators Class is to implement constructors for many common graphs, as well as thorough docstrings that can be used for reference.  The graph generators will grow as the Graph Theory Project does.  So please check back for additions and feel free to leave requests in the suggestions section.

We currently have 30 constructors of named graphs and basic structures.  Most of these graphs are constructed with a preset dictionary of x-y coordinates of each node.  This is advantageous for both style and time.  (The default graph plotting in SAGE uses the spring-layout algorithm).  SAGE graphs all have an associated graphics object, and examples of plotting options are shown on the graphs below.
 Line 9:
-Due to the volume of graphs now in the generators class, this wiki page is now intended to give status updates and serve as a gallery of graphs currently implemented.  To see information on a specific graph, run SAGE or the SAGE [http://sage.math.washington.edu:8100 notebook].  For a list of graph constructos, type "graphs." and hit tab.  For docstrings, type the graph name and one question mark (i.e.:  "graphs.!CubeGraph?") then shift + enter.  For source code, do likewise with two question marks.

The SAGE [http://sage.math.washington.edu:9001/graph Graph Theory Project] aims to implement Graph objects and algorithms in ["SAGE"].
+Due to the volume of graphs now in the generators class, this wiki page is now intended to give status updates and serve as a gallery of graphs currently implemented.  To see information on a specific graph, run SAGE or the SAGE [http://sage.math.washington.edu:8100 notebook].  For a list of graph constructors, type "graphs." and hit tab.  For docstrings, type the graph name and one question mark (i.e.:  "graphs.!CubeGraph?") then shift + enter.  For source code, do likewise with two question marks.
-Line 58:
+Line 56:
-}}}
+sage: flower_snark = graphs.FlowerSnark()
sage: flower_snark.set_boundary([15,16,17,18,19])
sage: flower_snark.show(figsize=[4,4], graph_border=True)
}}}
attachment:flower.png
 Line 64:
-}}}
+sage: frucht = graphs.FruchtGraph()
sage: frucht.show(figsize=[4,4], graph_border=True)
}}}
attachment:frucht.png
-Line 70:
+Line 71:
-}}}


=== Moebius Kantor ===
{{{

}}}
+sage: heawood = graphs.HeawoodGraph()
sage: heawood.show(figsize=[4,4], graph_border=True)
}}}
attachment:heawood.png


=== Möbius Kantor ===
{{{
sage: moebius_kantor = graphs.MoebiusKantorGraph()
sage: moebius_kantor.show(figsize=[4,4], graph_border=True)
}}}
attachment:moebiuskantor.png
-Line 82:
+Line 86:
-}}}
+sage: petersen = graphs.PetersenGraph()
sage: petersen.show(figsize=[4,4], graph_border=True)
}}}
attachment:petersen.png
-Line 88:
+Line 93:
-}}}
+sage: thomsen = graphs.ThomsenGraph()
sage: thomsen.show(figsize=[4,4], graph_border=True)
}}}
attachment:thomsen.png
-Line 96:
+Line 102:
-}}}
+sage: comp_bip_list = []
sage: for i in range (2):
... for j in range (4):
...  comp_bip_list.append(graphs.CompleteBipartiteGraph(i+3,j+1))
...
sage: graphs_list.show_graphs(comp_bip_list)
}}}
attachment:compbip.png
-Line 102:
+Line 113:
-}}}
+sage: comp_list = []
sage: for i in range(13)[1:]:
... comp_list.append(graphs.CompleteGraph(i))
...
sage: graphs_list.show_graphs(comp_list)
}}}
attachment:complete.png
-Line 108:
+Line 123:
-}}}
+sage: cube_list = []
sage: for i in range(6)[2:]:
... cube_list.append(graphs.CubeGraph(i))
...
sage: graphs_list.show_graphs(cube_list)
}}}
attachment:cube.png

{{{
sage: bigger_cube = graphs.CubeGraph(8)
sage: bigger_cube.show(figsize=[8,8], node_size=20, vertex_labels=False, graph_border=True)
}}}
attachment:biggercube.png
-Line 116:
+Line 141:
-}}}
+sage: barbell_list = []
sage: for i in range (4):
... for j in range (2):
...  barbell_list.append(graphs.BarbellGraph(i+3, j+2))
...
sage: graphs_list.show_graphs(barbell_list)
}}}
attachment:barbell.png
-Line 122:
+Line 152:
-}}}
+sage: bull = graphs.BullGraph()
sage: bull.show(figsize=[4,4], graph_border=True)
}}}
attachment:bull.png
-Line 128:
+Line 159:
-}}}
+sage: circ_ladder = graphs.CircularLadderGraph(9)
sage: circ_ladder.show(figsize=[4,4], graph_border=True)
}}}
attachment:circladder.png
-Line 134:
+Line 167:
-}}}
+sage: claw = graphs.ClawGraph()
sage: claw.show(figsize=[4,4], graph_border=True)
}}}
attachment:claw.png
-Line 140:
+Line 174:
-}}}
+sage: cycle = graphs.CycleGraph(17)
sage: cycle.show(figsize=[4,4], graph_border=True)
}}}
attachment:cycle.png
-Line 146:
+Line 181:
-}}}
+sage: diamond = graphs.DiamondGraph()
sage: diamond.show(figsize=[4,4], graph_border=True)
}}}
attachment:diamond.png
-Line 152:
+Line 188:
-}}}
+sage: dodecahedral = graphs.DodecahedralGraph()
sage: dodecahedral.show(figsize=[4,4], vertex_labels=False, node_size=50, graph_border=True)
}}}
attachment:dodecahedral.png
-Line 158:
+Line 196:
-}}}
+sage: empty = graphs.EmptyGraph()
sage: empty.show(figsize=[1,1], graph_border=True)
}}}
attachment:empty.png
-Line 164:
+Line 203:
-}}}
+sage: grid = graphs.Grid2dGraph(3,5)
sage: grid.show(figsize=[5,3])
}}}
attachment:grid.png
-Line 170:
+Line 210:
-}}}
+sage: house = graphs.HouseGraph()
sage: house.show(figsize=[4,4], graph_border=True)
}}}
attachment:house.png
-Line 176:
+Line 217:
-}}}
+sage: houseX = graphs.HouseXGraph()
sage: houseX.show(figsize=[4,4], graph_border=True)
}}}
attachment:housex.png
-Line 182:
+Line 224:
-}}}
+sage: krackhardt = graphs.KrackhardtKiteGraph()
sage: krackhardt.show(figsize=[4,4], graph_border=True)
}}}
attachment:krack.png
-Line 188:
+Line 231:
-}}}
+sage: ladder = graphs.LadderGraph(5)
sage: ladder.show(figsize=[4,4], graph_border=True)
}}}
attachment:ladder.png
-Line 194:
+Line 238:
-}}}
+sage: lollipop_list = []
sage: for i in range (4):
... for j in range (2):
...  lollipop_list.append(graphs.LollipopGraph(i+3, j+2))
...
sage: graphs_list.show_graphs(lollipop_list)
}}}
attachment:lollipop.png
-Line 200:
+Line 249:
-}}}
+sage: octahedral = graphs.OctahedralGraph()
sage: octahedral.show(figsize=[4,4], vertex_labels=False, node_size=50, graph_border=True)
}}}
attachment:octahedral.png
-Line 206:
+Line 257:
-}}}
+sage: path_line = graphs.PathGraph(5)
sage: path_circle = graphs.PathGraph(15)
sage: path_maze = graphs.PathGraph(45)
sage: path_list = [path_line, path_circle, path_maze]
sage: graphs_list.show_graphs(path_list)
}}}
attachment:path.png
-Line 212:
+Line 267:
-}}}
+sage: star_list = []
sage: for i in range (12)[4:]:
... star_list.append(graphs.StarGraph(i))
...
sage: graphs_list.show_graphs(star_list)
}}}
attachment:star.png
-Line 218:
+Line 277:
-}}}
+sage: tetrahedral = graphs.TetrahedralGraph()
sage: tetrahedral.show(figsize=[4,4], graph_border=True)
}}}
attachment:tetrahedral.png
-Line 224:
+Line 284:
-}}}
+sage: wheel_list = []
sage: for i in range (12)[4:]:
... wheel_list.append(graphs.WheelGraph(i))
...
sage: graphs_list.show_graphs(wheel_list)
}}}
attachment:wheel.png
-Line 231:
+Line 295:
-{{{

}}}
+Use for dense graphs:
{{{
time
sage: (graphs.RandomGNP(16,.77)).show(figsize=[4,4], graph_border=True)
}}}
My results:
CPU time: 0.74 s,  Wall time: 0.73 s
attachment:random.png
-Line 237:
+Line 305:
-{{{

}}}
+Use for sparse graphs:
{{{
time
sage: (graphs.RandomGNPFast(16,.19)).show(figsize=[4,4], graph_border=True)
}}}
My results:
CPU time: 0.63 s,  Wall time: 0.62 s
attachment:randomfast.png

Diff for "graph_generators"

Suggestions

Graphs I Plan to Add

Inherited from NetworkX

Families of Graphs

Named Graphs

Gallery of Graph Generators in SAGE

Named Graphs

Flower Snark

Frucht

Heawood

Möbius Kantor

Petersen

Thomsen

Graph Families

Complete Bipartite Graphs

Complete Graphs

Cube Graphs

Basic Structures

Barbell Graph

Bull Graph

Circular Ladder Graph

Claw Graph

Cycle Graphs

Diamond Graph

Dodecahedral Graph

Empty Graph

Grid 2d Graph

House Graph

House X Graph

Krackhardt Kite Graph

Ladder Graph

Lollipop Graph

Octahedral Graph

Path Graph

Star Graph

Tetrahedral Graph

Wheel Graph

Random Generators

Random GNP

Random GNP Fast