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"""
.. _tutorials-personalized_pagerank:
===============================
Personalized PageRank on a grid
===============================
This example demonstrates how to calculate and visualize personalized PageRank on a grid. We use the :meth:`igraph.Graph.personalized_pagerank` method, and demonstrate the effects on a grid graph.
"""
# %%
# .. note::
#
# The PageRank score of a vertex reflects the probability that a random walker will be at that vertex over the long run. At each step the walker has a 1 - damping chance to restart the walk and pick a starting vertex according to the probabilities defined in the reset vector.
import igraph as ig
import matplotlib.cm as cm
import matplotlib.pyplot as plt
import numpy as np
# %%
# We define a function that plots the graph on a Matplotlib axis, along with
# its personalized PageRank values. The function also generates a
# color bar on the side to see how the values change.
# We use `Matplotlib's Normalize class <https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.Normalize.html>`_
# to set the colors and ensure that our color bar range is correct.
def plot_pagerank(graph: ig.Graph, p_pagerank: list[float]):
"""Plots personalized PageRank values on a grid graph with a colorbar.
Parameters
----------
graph : ig.Graph
graph to plot
p_pagerank : list[float]
calculated personalized PageRank values
"""
# Create the axis for matplotlib
_, ax = plt.subplots(figsize=(8, 8))
# Create a matplotlib colormap
# coolwarm goes from blue (lowest value) to red (highest value)
cmap = cm.coolwarm
# Normalize the PageRank values for colormap
normalized_pagerank = ig.rescale(p_pagerank)
graph.vs["color"] = [cmap(pr) for pr in normalized_pagerank]
graph.vs["size"] = ig.rescale(p_pagerank, (20, 40))
graph.es["color"] = "gray"
graph.es["width"] = 1.5
# Plot the graph
ig.plot(graph, target=ax, layout=graph.layout_grid())
# Add a colorbar
sm = cm.ScalarMappable(norm=plt.Normalize(min(p_pagerank), max(p_pagerank)), cmap=cmap)
plt.colorbar(sm, ax=ax, label="Personalized PageRank")
plt.title("Graph with Personalized PageRank")
plt.axis("equal")
plt.show()
# %%
# First, we generate a graph, e.g. a Lattice Graph, which basically is a ``dim x dim`` grid:
dim = 5
grid_size = (dim, dim) # dim rows, dim columns
g = ig.Graph.Lattice(dim=grid_size, circular=False)
# %%
# Then we initialize the ``reset_vector`` (it's length should be equal to the number of vertices in the graph):
reset_vector = np.zeros(g.vcount())
# %%
# Then we set the nodes to prioritize, for example nodes with indices ``0`` and ``18``:
reset_vector[0] = 1
reset_vector[18] = 0.65
# %%
# Then we calculate the personalized PageRank:
personalized_page_rank = g.personalized_pagerank(damping=0.85, reset=reset_vector)
# %%
# Finally, we plot the graph with the personalized PageRank values:
plot_pagerank(g, personalized_page_rank)
# %%
# Alternatively, we can play around with the ``damping`` parameter:
personalized_page_rank = g.personalized_pagerank(damping=0.45, reset=reset_vector)
# %%
# Here we can see the same plot with the new damping parameter:
plot_pagerank(g, personalized_page_rank)
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