Python libraries NetworkX and matplotlib can be used to plot the complete graph. With n equal to one, it's a single point; with n equal to two, it's a line segment; with n equal to three, it's a triangle, but things get more intricate from there. With exceptionally large values of n (and an appropriate level of alpha that "lets the light shine through", so to speak), the patterns begin to resemble something like a mandala. This effect can be achieved like so, with n equal to 50 and alpha equal to 0.25:
import networkx as nx
import matplotlib.pyplot as plt
K = nx.complete_graph(50); pos = nx.circular_layout(K)
nx.draw_networkx(K, pos, with_labels=False, node_size=0, alpha=0.25); ax = plt.gca(); ax.set_axis_off(); plt.show()Closely related operations have been joined with semicolons so that the
parameters of n and alpha can be experimented upon in a Python shell easily.
Here is the output of the above code, rendered this time not by plt.show()
but by plt.savefig() with a high DPI setting (720):
The aesthetic qualities of the complete graph apparently have been known for hundreds of years, as demonstrated in this illustration from a 16th century edition of medieval Catalan philosopher Ramon Llull's Ars Magna:
