added changes requested in PR

Author: MBea13

doc/examples_sphinx-gallery/personalized_pagerank.py

@@ -8,19 +8,24 @@
 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
 
-import igraph as ig
-
-
 # %%
 # 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.
 
@@ -54,6 +59,7 @@ def plot_pagerank(graph: ig.Graph, p_pagerank: list[float]):
     plt.colorbar(sm, ax=ax, label="Personalized PageRank")
 
     plt.title("Graph with Personalized PageRank")
+    plt.axis("equal")
     plt.show()
 
 
@@ -68,14 +74,23 @@ def plot_pagerank(graph: ig.Graph, p_pagerank: list[float]):
 reset_vector = np.zeros(g.vcount())
 
 # %%
-# Then we set the nodes to prioritize, for example nodes with indices ``0`` and ``6``:
+# Then we set the nodes to prioritize, for example nodes with indices ``0`` and ``18``:
 reset_vector[0] = 1
-reset_vector[6] = 1
+reset_vector[18] = 0.65
 
 # %%
 # Then we calculate the personalized PageRank:
-personalized_page_rank = g.personalized_pagerank(weights=None, damping=0.85, reset=reset_vector)
+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)