Add rainbow coloring example to gallery. (#4330)

* Add rainbow coloring example to gallery.

Adds an example where edges on a complete graph are colored
by node distance.

* Update cycle fn param name.

* Update description and add link to article.

Co-authored-by: Jon Crall <erotemic@gmail.com>

Co-authored-by: Jon Crall <erotemic@gmail.com>

1 files changed, 68 insertions, 0 deletions

diff --git a/examples/drawing/plot_rainbow_coloring.py b/examples/drawing/plot_rainbow_coloring.py
new file mode 100644
index 00000000..1d9e6075
--- /dev/null
+++ b/examples/drawing/plot_rainbow_coloring.py
@@ -0,0 +1,68 @@
+"""
+================
+Rainbow Coloring
+================
+
+Generate a complete graph with 13 nodes in a circular layout with the
+edges colored by node distance. The node distance is given by the minimum
+number of nodes traversed along an arc between any two nodes on the circle.
+
+Such graphs are the subject of Ringel's conjecture, which states: any complete
+graph with ``2n + 1`` nodes can be tiled by any tree with ``n + 1`` nodes
+(i.e. copies of the tree can be placed over the complete graph such that each
+edge in the complete graph is covered exactly once). The edge coloring is
+helpful in determining how to place the tree copies.
+
+References
+----------
+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()