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"""
.. _tutorials-betweenness:
=======================
Betweenness
=======================
This example demonstrates how to visualize both vertex and edge betweenness with a custom defined color palette. We use the methods :meth:`igraph.GraphBase.betweenness` and :meth:`igraph.GraphBase.edge_betweenness` respectively, and demonstrate the effects on a standard `Krackhardt Kite <https://www.wikiwand.com/en/Krackhardt_kite_graph>`_ graph, as well as a `Watts-Strogatz <https://en.wikipedia.org/wiki/Watts%E2%80%93Strogatz_model>`_ random graph.
"""
import random
import matplotlib.pyplot as plt
from matplotlib.cm import ScalarMappable
from matplotlib.colors import LinearSegmentedColormap, Normalize
import igraph as ig
# %%
# We define a function that plots the graph on a Matplotlib axis, along with
# its vertex and edge betweenness values. The function also generates some
# color bars on the sides to see how they translate to each other. We use
# `Matplotlib's Normalize class <https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.Normalize.html>`_
# to ensure that our color bar ranges are correct, as well as *igraph*'s
# :meth:`igraph.utils.rescale` to rescale the betweennesses in the interval
# ``[0, 1]``.
def plot_betweenness(g, vertex_betweenness, edge_betweenness, ax, cax1, cax2):
'''Plot vertex/edge betweenness, with colorbars
Args:
g: the graph to plot.
ax: the Axes for the graph
cax1: the Axes for the vertex betweenness colorbar
cax2: the Axes for the edge betweenness colorbar
'''
# Rescale betweenness to be between 0.0 and 1.0
scaled_vertex_betweenness = ig.rescale(vertex_betweenness, clamp=True)
scaled_edge_betweenness = ig.rescale(edge_betweenness, clamp=True)
print(f"vertices: {min(vertex_betweenness)} - {max(vertex_betweenness)}")
print(f"edges: {min(edge_betweenness)} - {max(edge_betweenness)}")
# Define mappings betweenness -> color
cmap1 = LinearSegmentedColormap.from_list("vertex_cmap", ["pink", "indigo"])
cmap2 = LinearSegmentedColormap.from_list("edge_cmap", ["lightblue", "midnightblue"])
# Plot graph
g.vs["color"] = [cmap1(betweenness) for betweenness in scaled_vertex_betweenness]
g.vs["size"] = ig.rescale(vertex_betweenness, (10, 50))
g.es["color"] = [cmap2(betweenness) for betweenness in scaled_edge_betweenness]
g.es["width"] = ig.rescale(edge_betweenness, (0.5, 1.0))
ig.plot(
g,
target=ax,
layout="fruchterman_reingold",
vertex_frame_width=0.2,
)
# Color bars
norm1 = ScalarMappable(norm=Normalize(0, max(vertex_betweenness)), cmap=cmap1)
norm2 = ScalarMappable(norm=Normalize(0, max(edge_betweenness)), cmap=cmap2)
plt.colorbar(norm1, cax=cax1, orientation="horizontal", label='Vertex Betweenness')
plt.colorbar(norm2, cax=cax2, orientation="horizontal", label='Edge Betweenness')
# %%
# First, generate a graph, e.g. the Krackhardt Kite Graph:
random.seed(0)
g1 = ig.Graph.Famous("Krackhardt_Kite")
# %%
# Then we can compute vertex and edge betweenness:
vertex_betweenness1 = g1.betweenness()
edge_betweenness1 = g1.edge_betweenness()
# %% As a second example, we generate and analyze a Watts Strogatz graph:
g2 = ig.Graph.Watts_Strogatz(dim=1, size=150, nei=2, p=0.1)
vertex_betweenness2 = g2.betweenness()
edge_betweenness2 = g2.edge_betweenness()
# %%
# Finally, we plot the two graphs, each with two colorbars for vertex/edge
# betweenness
fig, axs = plt.subplots(
3, 2,
figsize=(7, 6),
gridspec_kw={"height_ratios": (20, 1, 1)},
)
plot_betweenness(g1, vertex_betweenness1, edge_betweenness1, *axs[:, 0])
plot_betweenness(g2, vertex_betweenness2, edge_betweenness2, *axs[:, 1])
fig.tight_layout(h_pad=1)
plt.show()
|
