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.

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 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"].

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

Moebius 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