Add "Visualizing Betweenness" tutorial

Documents how to visualize both vertex and edge betweenness

Author: Gomango999

doc/source/gallery.rst

@@ -9,6 +9,7 @@ Gallery
 This page contains short examples showcasing the functionality of |igraph|:
 
  - :ref:`tutorials-quickstart`
+ - :ref:`tutorials-betweenness`
  - :ref:`tutorials-bipartite-matching`
  - :ref:`tutorials-bipartite-matching-maxflow`
  - :ref:`tutorials-random`
@@ -25,6 +26,7 @@ This page contains short examples showcasing the functionality of |igraph|:
    :hidden:
 
    tutorials/quickstart/quickstart
+   tutorials/betweenness/betweenness
    tutorials/bipartite_matching/bipartite_matching
    tutorials/bipartite_matching_maxflow/bipartite_matching_maxflow
    tutorials/erdos_renyi/erdos_renyi

doc/source/tutorials/betweenness/assets/betweenness.py

@@ -0,0 +1,39 @@
+import igraph as ig
+import matplotlib.pyplot as plt
+import math
+import random
+
+# Generate graph
+random.seed(1)
+g = ig.Graph.Barabasi(n=200, m=2)
+
+# Calculate vertex betweenness and scale it to be between 0.0 and 1.0
+vertex_betweenness = g.betweenness()
+vertex_betweenness = [math.pow(i, 1/3) for i in vertex_betweenness] # scale values so transition is smoother
+min_vertex_betweenness = min(vertex_betweenness)
+max_vertex_betweenness = max(vertex_betweenness)
+vertex_betweenness = [(i - min_vertex_betweenness) / (max_vertex_betweenness - min_vertex_betweenness) for i in vertex_betweenness]
+
+# Calculate edge betweenness and scale it to be between 0.0 and 1.0
+edge_betweenness = g.edge_betweenness()
+edge_betweenness = [math.pow(i, 1/2) for i in edge_betweenness] # scale values so transition is smoother
+min_edge_betweenness = min(edge_betweenness)
+max_edge_betweenness = max(edge_betweenness)
+edge_betweenness = [(i - min_edge_betweenness) / (max_edge_betweenness - min_edge_betweenness) for i in edge_betweenness]
+
+# Plot the graph
+fig, ax = plt.subplots()
+ig.plot(
+    g, 
+    target=ax, 
+    layout="fruchterman_reingold",
+    palette=ig.GradientPalette("white", "midnightblue"),
+    vertex_color=[int(betweenness * 255) for betweenness in vertex_betweenness], # colors are integers between 0 and 255
+    edge_color=[int(betweenness * 255) for betweenness in edge_betweenness],
+    vertex_size=[betweenness*0.5+0.1 for betweenness in vertex_betweenness], # vertex_size is between 0.1 and 0.6
+    edge_width=[betweenness*0.5+0.5 for betweenness in edge_betweenness], # edge_width is between 0.5 and 1
+    vertex_frame_width=0.2,
+)
+plt.show()
+
+# fig.savefig("../figures/betweenness.png", dpi=200)

doc/source/tutorials/betweenness/betweenness.rst

@@ -0,0 +1,63 @@
+.. include:: ../../include/global.rst
+
+.. _tutorials-betweenness:
+
+=======================
+Visualizing Betweenness
+=======================
+
+.. _betweenness: https://igraph.org/python/doc/api/igraph._igraph.GraphBase.html#betweenness
+.. |betweenness| replace:: :meth:`betweenness`
+.. _edge_betweenness: https://igraph.org/python/doc/api/igraph._igraph.GraphBase.html#edge_betweenness
+.. |edge_betweenness| replace:: :meth:`edge_betweenness`
+
+This example will demonstrate how to visualize both vertex and edge betweenness with a custom defined color palette. We use the methods |betweenness|_ and |edge_betweenness|_ respectively.
+
+.. code-block:: python
+
+    import igraph as ig
+    import matplotlib.pyplot as plt
+    import math
+    import random
+
+    # Generate graph
+    random.seed(1)
+    g = ig.Graph.Barabasi(n=200, m=2)
+
+    # Calculate vertex betweenness and scale it to be between 0.0 and 1.0
+    vertex_betweenness = g.betweenness()
+    vertex_betweenness = [math.pow(i, 1/3) for i in vertex_betweenness] 
+    min_vertex_betweenness = min(vertex_betweenness)
+    max_vertex_betweenness = max(vertex_betweenness)
+    vertex_betweenness = [(i - min_vertex_betweenness) / (max_vertex_betweenness - min_vertex_betweenness) for i in vertex_betweenness]
+
+    # Calculate edge betweenness and scale it to be between 0.0 and 1.0
+    edge_betweenness = g.edge_betweenness()
+    edge_betweenness = [math.pow(i, 1/2) for i in edge_betweenness] 
+    min_edge_betweenness = min(edge_betweenness)
+    max_edge_betweenness = max(edge_betweenness)
+    edge_betweenness = [(i - min_edge_betweenness) / (max_edge_betweenness - min_edge_betweenness) for i in edge_betweenness]
+
+    # Plot the graph
+    fig, ax = plt.subplots()
+    ig.plot(
+        g, 
+        target=ax, 
+        layout="fruchterman_reingold",
+        palette=ig.GradientPalette("white", "midnightblue"), # define a new color palette
+        vertex_color=[int(betweenness * 255) for betweenness in vertex_betweenness], # colors are integers between 0 and 255
+        edge_color=[int(betweenness * 255) for betweenness in edge_betweenness],
+        vertex_size=[betweenness*0.5+0.1 for betweenness in vertex_betweenness], # vertex_size is between 0.1 and 0.6
+        edge_width=[betweenness*0.5+0.5 for betweenness in edge_betweenness], # edge_width is between 0.5 and 1
+        vertex_frame_width=0.2,
+    )
+    plt.show()
+
+Note that we scale the betweennesses for the vertices and edges by the cube root and square root respectively. The choice of scaling is arbitrary, but is used to give a smoother, more linear transition in the sizes and colors of nodes and edges. The final output graph is here:
+
+.. figure:: ./figures/betweenness.png
+   :alt: A graph visualizing the betweenness of each vertex and edge.
+   :align: center
+
+   A graph visualizing edge betweenness. White indicates a low betweenness centrality, whereas dark blue indicates a high betweenness centrality.
+