Dense connectivity in complex networks often conceals meaningful organization. Backbone extraction mitigates this by filtering edges to retain the most informative connections. Similarity-based approaches rank edges using topological similarity functions but are typically limited to pairwise graphs. This study compares pairwise and high-order similarity backbones to examine how multi-node relations influence network filtering. Both frameworks share the same similarity principle but differ in how similarity is computed and propagated: the pairwise formulation evaluates dyadic relations, whereas the high-order formulation derives edge scores from simplex-level similarity within simplicial complexes. Experiments on five real datasets show partial rank agreement between the two, with the largest deviations observed under strong filtering. Topological analysis reveals that high-order backbones preserve higher reachability and more unique simplices, while pairwise backbones maintain greater transitivity. These findings demonstrate that higher-order and pairwise similarity backbones capture complementary aspects of network structure.

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High-Order Vs. Pairwise Similarity Backbones: A Comparative Analysis

  • Ali Yassin,
  • Mohamad Ali Tarekh,
  • Hocine Cherifi,
  • Hamida Seba,
  • Olivier Togni,
  • Ali Jaber

摘要

Dense connectivity in complex networks often conceals meaningful organization. Backbone extraction mitigates this by filtering edges to retain the most informative connections. Similarity-based approaches rank edges using topological similarity functions but are typically limited to pairwise graphs. This study compares pairwise and high-order similarity backbones to examine how multi-node relations influence network filtering. Both frameworks share the same similarity principle but differ in how similarity is computed and propagated: the pairwise formulation evaluates dyadic relations, whereas the high-order formulation derives edge scores from simplex-level similarity within simplicial complexes. Experiments on five real datasets show partial rank agreement between the two, with the largest deviations observed under strong filtering. Topological analysis reveals that high-order backbones preserve higher reachability and more unique simplices, while pairwise backbones maintain greater transitivity. These findings demonstrate that higher-order and pairwise similarity backbones capture complementary aspects of network structure.