Add example of spectral embedding of the grid graph (#2690)

1 files changed, 61 insertions, 0 deletions

diff --git a/examples/drawing/plot_spectral_grid.py b/examples/drawing/plot_spectral_grid.py
new file mode 100644
index 00000000..3f2bc922
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+++ b/examples/drawing/plot_spectral_grid.py
@@ -0,0 +1,61 @@
+"""
+==================
+Spectral Embedding
+==================
+
+The spectral layout positions the nodes of the graph based on the
+eigenvectors of the graph Laplacian $L = D - A$, where $A$ is the
+adjacency matrix and $D$ is the degree matrix of the graph.
+By default, the spectral layout will embed the graph in two
+dimensions (you can embed your graph in other dimensions using the
+``dim`` argument to either :func:`~drawing.nx_pylab.draw_spectral` or
+:func:`~drawing.layout.spectral_layout`).
+
+When the edges of the graph represent similarity between the incident
+nodes, the spectral embedding will place highly similar nodes closer
+to one another than nodes which are less similar.
+
+This is particularly striking when you spectrally embed a grid
+graph.  In the full grid graph, the nodes in the center of the
+graph are pulled apart more than nodes on the periphery.
+As you remove internal nodes, this effect increases.
+"""
+
+import matplotlib.pyplot as plt
+import networkx as nx
+
+
+options = {
+    'node_color': 'C0',
+    'node_size': 100,
+}
+
+G = nx.grid_2d_graph(6, 6)
+plt.subplot(332)
+nx.draw_spectral(G, **options)
+
+G.remove_edge((2, 2), (2, 3))
+plt.subplot(334)
+nx.draw_spectral(G, **options)
+
+G.remove_edge((3, 2), (3, 3))
+plt.subplot(335)
+nx.draw_spectral(G, **options)
+
+G.remove_edge((2, 2), (3, 2))
+plt.subplot(336)
+nx.draw_spectral(G, **options)
+
+G.remove_edge((2, 3), (3, 3))
+plt.subplot(337)
+nx.draw_spectral(G, **options)
+
+G.remove_edge((1, 2), (1, 3))
+plt.subplot(338)
+nx.draw_spectral(G, **options)
+
+G.remove_edge((4, 2), (4, 3))
+plt.subplot(339)
+nx.draw_spectral(G, **options)
+
+plt.show()