Kirchhoffian indices for weighted digraphs

Bianchi, Monica; Palacios, José Luis; Torriero, Anna and Wirkierman, Ariel Luis. 2019. Kirchhoffian indices for weighted digraphs. Discrete Applied Mathematics, 255, pp. 142-154. ISSN 0166-218X [Article]

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Abstract or Description

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 MoorePenrose 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.

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Identification Number (DOI):


Kirchhoff index, Random walk on graphs, Weighted digraphs, Moore-Penrose inverse

Departments, Centres and Research Units:

Institute of Management Studies
Institute of Management Studies > Structural Economic Analysis


13 August 2018Accepted
11 October 2018Published Online
28 February 2019Published

Item ID:


Date Deposited:

08 Oct 2018 11:25

Last Modified:

26 Feb 2024 13:35

Peer Reviewed:

Yes, this version has been peer-reviewed.


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