74 lines
2.1 KiB
Python
74 lines
2.1 KiB
Python
|
"""
|
||
|
|
=====
|
||
|
|
Atlas
|
||
|
|
=====
|
||
|
|
|
||
|
|
Atlas of all graphs of 6 nodes or less.
|
||
|
|
"""
|
||
|
|
|
||
|
|
import random
|
||
|
|
|
||
|
|
# This example needs Graphviz and either PyGraphviz or pydot.
|
||
|
|
# from networkx.drawing.nx_pydot import graphviz_layout
|
||
|
|
from networkx.drawing.nx_agraph import graphviz_layout
|
||
|
|
|
||
|
|
import matplotlib.pyplot as plt
|
||
|
|
|
||
|
|
import networkx as nx
|
||
|
|
from networkx.algorithms.isomorphism.isomorph import (
|
||
|
|
graph_could_be_isomorphic as isomorphic,
|
||
|
|
)
|
||
|
|
from networkx.generators.atlas import graph_atlas_g
|
||
|
|
|
||
|
|
|
||
|
|
def atlas6():
|
||
|
|
""" Return the atlas of all connected graphs of 6 nodes or less.
|
||
|
|
Attempt to check for isomorphisms and remove.
|
||
|
|
"""
|
||
|
|
|
||
|
|
Atlas = graph_atlas_g()[0:208] # 208
|
||
|
|
# remove isolated nodes, only connected graphs are left
|
||
|
|
U = nx.Graph() # graph for union of all graphs in atlas
|
||
|
|
for G in Atlas:
|
||
|
|
zerodegree = [n for n in G if G.degree(n) == 0]
|
||
|
|
for n in zerodegree:
|
||
|
|
G.remove_node(n)
|
||
|
|
U = nx.disjoint_union(U, G)
|
||
|
|
|
||
|
|
# iterator of graphs of all connected components
|
||
|
|
C = (U.subgraph(c) for c in nx.connected_components(U))
|
||
|
|
|
||
|
|
UU = nx.Graph()
|
||
|
|
# do quick isomorphic-like check, not a true isomorphism checker
|
||
|
|
nlist = [] # list of nonisomorphic graphs
|
||
|
|
for G in C:
|
||
|
|
# check against all nonisomorphic graphs so far
|
||
|
|
if not iso(G, nlist):
|
||
|
|
nlist.append(G)
|
||
|
|
UU = nx.disjoint_union(UU, G) # union the nonisomorphic graphs
|
||
|
|
return UU
|
||
|
|
|
||
|
|
|
||
|
|
def iso(G1, glist):
|
||
|
|
"""Quick and dirty nonisomorphism checker used to check isomorphisms."""
|
||
|
|
for G2 in glist:
|
||
|
|
if isomorphic(G1, G2):
|
||
|
|
return True
|
||
|
|
return False
|
||
|
|
|
||
|
|
|
||
|
|
G = atlas6()
|
||
|
|
|
||
|
|
print(f"graph has {nx.number_of_nodes(G)} nodes with {nx.number_of_edges(G)} edges")
|
||
|
|
print(nx.number_connected_components(G), "connected components")
|
||
|
|
|
||
|
|
plt.figure(1, figsize=(8, 8))
|
||
|
|
# layout graphs with positions using graphviz neato
|
||
|
|
pos = graphviz_layout(G, prog="neato")
|
||
|
|
# color nodes the same in each connected subgraph
|
||
|
|
C = (G.subgraph(c) for c in nx.connected_components(G))
|
||
|
|
for g in C:
|
||
|
|
c = [random.random()] * nx.number_of_nodes(g) # random color...
|
||
|
|
nx.draw(g, pos, node_size=40, node_color=c, vmin=0.0, vmax=1.0, with_labels=False)
|
||
|
|
plt.show()
|