Returnability in complex directed networks (digraphs)

Ernesto Estrada, Naomichi Hatano

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12 Citations (Scopus)
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The concept of returnability is proposed for complex directed networks (digraphs). It can be seen as a generalization of the concept of reciprocity. Two measures of the returnability are introduced. We establish closed formulas for the calculation of the returnability measures, which are also related to the digraph spectrum. The two measures are calculated for simple examples of digraphs as well as for real-world complex directed networks and are compared with the reciprocity.
Original languageEnglish
Pages (from-to)1886-1896
Number of pages10
JournalLinear Algebra and its Applications
Publication statusPublished - 2009


  • graph spectrum
  • digraphs
  • estrada index
  • reciprocity
  • complex networks


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