Atlas of all connected graphs with up to 6 nodes.
This example uses Graphviz via PyGraphviz.
The image should show 142 graphs. We don’t plot the empty graph nor the single node graph. (142 is the sum of values 2 to n=6 in sequence oeis.org/A001349).
Graph named 'G208' with 809 nodes and 1112 edges 142 connected components
import random import matplotlib.pyplot as plt import networkx as nx GraphMatcher = nx.isomorphism.vf2userfunc.GraphMatcher def atlas6(): """Return the atlas of all connected graphs with at most 6 nodes""" Atlas = nx.graph_atlas_g()[3:209] # 0, 1, 2 => no edges. 208 is last 6 node graph U = nx.Graph() # graph for union of all graphs in atlas for G in Atlas: # check if connected if nx.number_connected_components(G) == 1: # check if isomorphic to a previous graph if not GraphMatcher(U, G).subgraph_is_isomorphic(): U = nx.disjoint_union(U, G) return U G = atlas6() print(G) print(nx.number_connected_components(G), "connected components") plt.figure(1, figsize=(8, 8)) # layout graphs with positions using graphviz neato pos = nx.nx_agraph.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()
Total running time of the script: ( 0 minutes 4.690 seconds)