Journal article

The mathematics of non-linear metrics for nested networks

  • Wu, Rui-Jie Department of Physics, University of Fribourg, Switzerland
  • Shi, Gui-Yuan Department of Physics, University of Fribourg, Switzerland
  • Zhang, Yi-Cheng Department of Physics, University of Fribourg, Switzerland - Institute of Fundamental and Frontier Sciences, UESTC, Chengdu, China
  • Mariani, Manuel Sebastian Department of Physics, University of Fribourg, Switzerland
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    15.10.2016
Published in:
  • Physica A: Statistical Mechanics and its Applications. - 2016, vol. 460, p. 254–269
English Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness–complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness– complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness–complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.
Faculty
Faculté des sciences et de médecine
Department
Département de Physique
Language
  • English
Classification
Physics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/304958
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