graph theory.sagews

Sage is extremely powerful for graph theory...

See the reference manual on graph theory

G = graphs.HouseGraph()
G.plot().save('graph.pdf')

graphs.[tab key]

G = graphs.PetersenGraph()
G.show(vertex_colors=G.coloring(hex_colors=True))

H = G.automorphism_group()
show(H)

$\displaystyle \langle (3,7)(4,5)(8,9), (2,6)(3,8)(4,5)(7,9), (1,4,5)(2,3,8,6,9,7), (0,1)(2,4,6,5)(3,9,8,7) \rangle$

H.order()

120

%md
There is also interactive plotting, but it doesn't support colors (yet):

There is also interactive plotting, but it doesn't support colors (yet):

show(G)

d3-based renderer not yet implemented

G = graphs.PappusGraph()
G.show(vertex_colors=G.coloring(hex_colors=True))

C = graphs.CubeGraph(9)
color = {}
for v in C.vertices():
    b = v.count('1')/9
    g = 1 - b
    if (0, g, b) in color: color[(0, g, b)].append(v)
    else: color[(0, g, b)] = [v]
C.show(vertex_labels=False, graph_border=True, vertex_colors=color, figsize=[9,8])

# Try typing "graphs.[tab key]"... and "graphs.something([tab key]"