彩虹上色

在圆形布局中生成包含13个节点的完整图形，其边按节点距离着色。节点距离由圆上任意两个节点之间的弧线上穿过的最小节点数确定。

这样的图是林格尔猜想的主题，该猜想指出：任何有 2n + 1 任何树都可以平铺节点， n + 1 节点(即，可以将树的副本放置在完整图上，使得完整图中的每条边恰好被覆盖一次)。边缘着色对于确定如何放置树副本很有帮助。

参考文献

https://www.quantamagazine.org/mathematicians-prove-ringels-graph-theory-conjecture-20200219/

import matplotlib.pyplot as plt
import networkx as nx

# A rainbow color mapping using matplotlib's tableau colors
node_dist_to_color = {
    1: "tab:red",
    2: "tab:orange",
    3: "tab:olive",
    4: "tab:green",
    5: "tab:blue",
    6: "tab:purple",
}

# Create a complete graph with an odd number of nodes
nnodes = 13
G = nx.complete_graph(nnodes)

# A graph with (2n + 1) nodes requires n colors for the edges
n = (nnodes - 1) // 2
ndist_iter = list(range(1, n + 1))

# Take advantage of circular symmetry in determining node distances
ndist_iter += ndist_iter[::-1]


def cycle(nlist, n):
    return nlist[-n:] + nlist[:-n]


# Rotate nodes around the circle and assign colors for each edge based on
# node distance
nodes = list(G.nodes())
for i, nd in enumerate(ndist_iter):
    for u, v in zip(nodes, cycle(nodes, i + 1)):
        G[u][v]["color"] = node_dist_to_color[nd]

pos = nx.circular_layout(G)
# Create a figure with 1:1 aspect ratio to preserve the circle.
fig, ax = plt.subplots(figsize=(8, 8))
node_opts = {"node_size": 500, "node_color": "w", "edgecolors": "k", "linewidths": 2.0}
nx.draw_networkx_nodes(G, pos, **node_opts)
nx.draw_networkx_labels(G, pos, font_size=14)
# Extract color from edge data
edge_colors = [edgedata["color"] for _, _, edgedata in G.edges(data=True)]
nx.draw_networkx_edges(G, pos, width=2.0, edge_color=edge_colors)

ax.set_axis_off()
fig.tight_layout()
plt.show()