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Resolution of ranking hierarchies in directed networks

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  • Elisa Letizia
  • Paolo Barucca
  • Fabrizio Lillo

Abstract

Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.

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  • Elisa Letizia & Paolo Barucca & Fabrizio Lillo, 2018. "Resolution of ranking hierarchies in directed networks," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-25, February.
    • Handle: RePEc:plo:pone00:0191604
    DOI: 10.1371/journal.pone.0191604
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    References listed on IDEAS

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    1. KICHIKAWA Yuichi & IINO Takashi & IYETOMI Hiroshi & INOUE Hiroyasu, 2019. "Hierarchical and Circular Flow Structure of the Interfirm Transaction Network in Japan," Discussion papers 19063, Research Institute of Economy, Trade and Industry (RIETI).

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