Graph Comparison Gallery ======================== This gallery compares each backbone method against a reference graph. Removed nodes are colored red and retained edges are drawn as thicker black lines. For readability, isolates are removed from each backbone before plotting. Les Miserables (Non-Bipartite Methods) -------------------------------------- Glab Filter ^^^^^^^^^^^ - Module: ``hybrid`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``6`` nodes, ``5`` edges - Nodes removed: ``71`` .. image:: /_static/graph_gallery/les_miserables/glab_filter.png :width: 800px :alt: Backbone comparison visualization Adamic Adar Index ^^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``26`` nodes, ``76`` edges - Nodes removed: ``51`` .. image:: /_static/graph_gallery/les_miserables/adamic_adar_index.png :width: 800px :alt: Backbone comparison visualization Cosine Backbone ^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``27`` nodes, ``76`` edges - Nodes removed: ``50`` .. image:: /_static/graph_gallery/les_miserables/cosine_backbone.png :width: 800px :alt: Backbone comparison visualization Dice Backbone ^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``27`` nodes, ``76`` edges - Nodes removed: ``50`` .. image:: /_static/graph_gallery/les_miserables/dice_backbone.png :width: 800px :alt: Backbone comparison visualization Graph Distance Proximity ^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``51`` nodes, ``76`` edges - Nodes removed: ``26`` .. image:: /_static/graph_gallery/les_miserables/graph_distance_proximity.png :width: 800px :alt: Backbone comparison visualization Hub Depressed Index ^^^^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``29`` nodes, ``76`` edges - Nodes removed: ``48`` .. image:: /_static/graph_gallery/les_miserables/hub_depressed_index.png :width: 800px :alt: Backbone comparison visualization Hub Promoted Index ^^^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``26`` nodes, ``76`` edges - Nodes removed: ``51`` .. image:: /_static/graph_gallery/les_miserables/hub_promoted_index.png :width: 800px :alt: Backbone comparison visualization Jaccard Backbone ^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``27`` nodes, ``76`` edges - Nodes removed: ``50`` .. image:: /_static/graph_gallery/les_miserables/jaccard_backbone.png :width: 800px :alt: Backbone comparison visualization Lhn Local Index ^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``39`` nodes, ``76`` edges - Nodes removed: ``38`` .. image:: /_static/graph_gallery/les_miserables/lhn_local_index.png :width: 800px :alt: Backbone comparison visualization Local Path Index ^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``24`` nodes, ``76`` edges - Nodes removed: ``53`` .. image:: /_static/graph_gallery/les_miserables/local_path_index.png :width: 800px :alt: Backbone comparison visualization Neighborhood Overlap ^^^^^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``22`` nodes, ``76`` edges - Nodes removed: ``55`` .. image:: /_static/graph_gallery/les_miserables/neighborhood_overlap.png :width: 800px :alt: Backbone comparison visualization Preferential Attachment Score ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``33`` nodes, ``76`` edges - Nodes removed: ``44`` .. image:: /_static/graph_gallery/les_miserables/preferential_attachment_score.png :width: 800px :alt: Backbone comparison visualization Resource Allocation Index ^^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``proximity`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``33`` nodes, ``76`` edges - Nodes removed: ``44`` .. image:: /_static/graph_gallery/les_miserables/resource_allocation_index.png :width: 800px :alt: Backbone comparison visualization Disparity Filter ^^^^^^^^^^^^^^^^ - Module: ``statistical`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``10`` nodes, ``9`` edges - Nodes removed: ``67`` .. image:: /_static/graph_gallery/les_miserables/disparity_filter.png :width: 800px :alt: Backbone comparison visualization Ecm Filter ^^^^^^^^^^ - Module: ``statistical`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``254`` edges - Nodes removed: ``0`` - Validation warning: ``Filtered edge count equals the original graph. Re-test and validate this method's threshold or parameters.`` .. image:: /_static/graph_gallery/les_miserables/ecm_filter.png :width: 800px :alt: Backbone comparison visualization Lans Filter ^^^^^^^^^^^ - Module: ``statistical`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``109`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/lans_filter.png :width: 800px :alt: Backbone comparison visualization Marginal Likelihood Filter ^^^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``statistical`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``58`` nodes, ``70`` edges - Nodes removed: ``19`` .. image:: /_static/graph_gallery/les_miserables/marginal_likelihood_filter.png :width: 800px :alt: Backbone comparison visualization Multiple Linkage Analysis ^^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``statistical`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``109`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/multiple_linkage_analysis.png :width: 800px :alt: Backbone comparison visualization Noise Corrected Filter ^^^^^^^^^^^^^^^^^^^^^^ - Module: ``statistical`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``70`` nodes, ``98`` edges - Nodes removed: ``7`` .. image:: /_static/graph_gallery/les_miserables/noise_corrected_filter.png :width: 800px :alt: Backbone comparison visualization Doubly Stochastic Filter ^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``109`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/doubly_stochastic_filter.png :width: 800px :alt: Backbone comparison visualization Edge Betweenness Filter ^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``77`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/edge_betweenness_filter.png :width: 800px :alt: Backbone comparison visualization Global Sparsification ^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``44`` nodes, ``102`` edges - Nodes removed: ``33`` .. image:: /_static/graph_gallery/les_miserables/global_sparsification.png :width: 800px :alt: Backbone comparison visualization Global Threshold Filter ^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``58`` nodes, ``157`` edges - Nodes removed: ``19`` .. image:: /_static/graph_gallery/les_miserables/global_threshold_filter.png :width: 800px :alt: Backbone comparison visualization H Backbone ^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``19`` nodes, ``22`` edges - Nodes removed: ``58`` .. image:: /_static/graph_gallery/les_miserables/h_backbone.png :width: 800px :alt: Backbone comparison visualization High Salience Skeleton ^^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``76`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/high_salience_skeleton.png :width: 800px :alt: Backbone comparison visualization Maximum Spanning Tree Backbone ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``76`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/maximum_spanning_tree_backbone.png :width: 800px :alt: Backbone comparison visualization Metric Backbone ^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``163`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/metric_backbone.png :width: 800px :alt: Backbone comparison visualization Modularity Backbone ^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``44`` nodes, ``72`` edges - Nodes removed: ``33`` .. image:: /_static/graph_gallery/les_miserables/modularity_backbone.png :width: 800px :alt: Backbone comparison visualization Node Degree Filter ^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``60`` nodes, ``237`` edges - Nodes removed: ``17`` .. image:: /_static/graph_gallery/les_miserables/node_degree_filter.png :width: 800px :alt: Backbone comparison visualization Planar Maximally Filtered Graph ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``162`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/planar_maximally_filtered_graph.png :width: 800px :alt: Backbone comparison visualization Primary Linkage Analysis ^^^^^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``69`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/primary_linkage_analysis.png :width: 800px :alt: Backbone comparison visualization Strongest N Ties ^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``113`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/strongest_n_ties.png :width: 800px :alt: Backbone comparison visualization Ultrametric Backbone ^^^^^^^^^^^^^^^^^^^^ - Module: ``structural`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``118`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/ultrametric_backbone.png :width: 800px :alt: Backbone comparison visualization Local Degree ^^^^^^^^^^^^ - Module: ``unweighted`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``135`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/local_degree.png :width: 800px :alt: Backbone comparison visualization Lspar ^^^^^ - Module: ``unweighted`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``136`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/lspar.png :width: 800px :alt: Backbone comparison visualization Sparsify ^^^^^^^^ - Module: ``unweighted`` - Original graph: ``77`` nodes, ``254`` edges - Backbone graph: ``77`` nodes, ``136`` edges - Nodes removed: ``0`` .. image:: /_static/graph_gallery/les_miserables/sparsify.png :width: 800px :alt: Backbone comparison visualization Davis Southern Women (Bipartite Methods) ---------------------------------------- Fdsm ^^^^ - Module: ``bipartite`` - Original graph: ``18`` nodes, ``153`` edges - Backbone graph: ``11`` nodes, ``9`` edges - Nodes removed: ``7`` .. image:: /_static/graph_gallery/southern_women/fdsm.png :width: 800px :alt: Backbone comparison visualization Fixedcol ^^^^^^^^ - Module: ``bipartite`` - Original graph: ``18`` nodes, ``153`` edges - Backbone graph: ``7`` nodes, ``9`` edges - Nodes removed: ``11`` .. image:: /_static/graph_gallery/southern_women/fixedcol.png :width: 800px :alt: Backbone comparison visualization Fixedfill ^^^^^^^^^ - Module: ``bipartite`` - Original graph: ``18`` nodes, ``153`` edges - Backbone graph: ``7`` nodes, ``9`` edges - Nodes removed: ``11`` .. image:: /_static/graph_gallery/southern_women/fixedfill.png :width: 800px :alt: Backbone comparison visualization Fixedrow ^^^^^^^^ - Module: ``bipartite`` - Original graph: ``18`` nodes, ``153`` edges - Backbone graph: ``16`` nodes, ``17`` edges - Nodes removed: ``2`` .. image:: /_static/graph_gallery/southern_women/fixedrow.png :width: 800px :alt: Backbone comparison visualization Sdsm ^^^^ - Module: ``bipartite`` - Original graph: ``18`` nodes, ``153`` edges - Backbone graph: ``6`` nodes, ``3`` edges - Nodes removed: ``12`` .. image:: /_static/graph_gallery/southern_women/sdsm.png :width: 800px :alt: Backbone comparison visualization