Kirchhoffian indices for weighted digraphs

Monica Bianchi, José Luis Palacios, Anna Torriero, Ariel Luis Wirkierman

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review


The resistance indices, namely the Kirchhoff index and its generalisations, have undergone intense critical scrutiny in recent years. Based on random walks, we derive three Kirchhoffian indices for strongly connected and weighted digraphs. These indices are expressed in terms of (i) hitting times and (ii) the trace and eigenvalues of suitable matrices associated to the graph, namely the asymmetric Laplacian, the diagonally scaled Laplacian and their Moore–Penrose inverses. The appropriateness of the generalised Kirchhoff index as a measure of network robustness is discussed, providing an alternative interpretation which is supported by an empirical application to the World Trade Network.
Lingua originaleEnglish
pagine (da-a)142-154
Numero di pagine13
RivistaDiscrete Applied Mathematics
Stato di pubblicazionePubblicato - 2019


  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Kirchhoff index
  • Moore–Penrose inverse
  • Random walk on graphs
  • Weighted digraphs


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