.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "tutorials/betweenness.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_tutorials_betweenness.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_tutorials_betweenness.py:


.. _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.

.. GENERATED FROM PYTHON SOURCE LINES 11-18

.. code-block:: Python

    import random
    import matplotlib.pyplot as plt
    from matplotlib.cm import ScalarMappable
    from matplotlib.colors import LinearSegmentedColormap, Normalize
    import igraph as ig









.. GENERATED FROM PYTHON SOURCE LINES 19-26

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]``.

.. GENERATED FROM PYTHON SOURCE LINES 26-65

.. code-block:: Python

    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")









.. GENERATED FROM PYTHON SOURCE LINES 66-67

First, generate a graph, e.g. the Krackhardt Kite Graph:

.. GENERATED FROM PYTHON SOURCE LINES 67-70

.. code-block:: Python

    random.seed(0)
    g1 = ig.Graph.Famous("Krackhardt_Kite")








.. GENERATED FROM PYTHON SOURCE LINES 71-72

Then we can compute vertex and edge betweenness:

.. GENERATED FROM PYTHON SOURCE LINES 72-75

.. code-block:: Python

    vertex_betweenness1 = g1.betweenness()
    edge_betweenness1 = g1.edge_betweenness()








.. GENERATED FROM PYTHON SOURCE LINES 76-80

.. code-block:: Python

    g2 = ig.Graph.Watts_Strogatz(dim=1, size=150, nei=2, p=0.1)
    vertex_betweenness2 = g2.betweenness()
    edge_betweenness2 = g2.edge_betweenness()








.. GENERATED FROM PYTHON SOURCE LINES 81-83

Finally, we plot the two graphs, each with two colorbars for vertex/edge
betweenness

.. GENERATED FROM PYTHON SOURCE LINES 83-92

.. code-block:: Python

    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()



.. image-sg:: /tutorials/images/sphx_glr_betweenness_001.png
   :alt: betweenness
   :srcset: /tutorials/images/sphx_glr_betweenness_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    vertices: 0.0 - 14.0
    edges: 1.5 - 16.0
    vertices: 0.0 - 753.8235063912693
    edges: 8.951984126984126 - 477.30745059034535





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.179 seconds)


.. _sphx_glr_download_tutorials_betweenness.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: betweenness.ipynb <betweenness.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: betweenness.py <betweenness.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: betweenness.zip <betweenness.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_