.. _sphx_glr_api_gallery_graph_theory_spectral:

Spectral graph theory
-----------------------

The graph Laplacian, algebraic connectivity, and spectral bipartition.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Two dense clusters joined by a single bridge edge -- a case where the Fiedler vector&#x27;s sign cleanly recovers the two clusters, and the small algebraic connectivity reflects how easily the graph is disconnected (by removing just the bridge).">

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  .. image:: /api/gallery/graph_theory/spectral/images/thumb/sphx_glr_plot_01_barbell_bipartition_thumb.png
    :alt:

  :doc:`/api/gallery/graph_theory/spectral/plot_01_barbell_bipartition`

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      <div class="sphx-glr-thumbnail-title">Fiedler's spectral bipartition of a "barbell" graph</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/graph_theory/spectral/plot_01_barbell_bipartition