A novel measure of edge and vertex centrality for assessing robustness in complex networks

  • G. P. ClementeEmail author
  • A. Cornaro


In this work, we propose a novel robustness measure for networks, which we refer to as Effective Resistance Centrality of a vertex (or an edge), defined as the relative drop of the Kirchhoff index due to deletion of this vertex (edge) from the network. Indeed, we provide a local robustness measure, able to catch which is the effect of either a specific vertex or a specific edge on the network robustness. The validness of this new measure is illustrated on some typical graphs and on a wide variety of well-known model networks. Furthermore, we analyse the topology of the US domestic flight connections. In particular, we investigate the role that airports play in maintaining the structure of the entire network.


Robustness Kirchhoff index Complex networks Air transportation networks Spatial economics 



We would like to thank the editor, the guest editor of the Special Issue “Dynamics of socio-economic systems” and the anonymous referees for their careful reviews on a previous version of this paper. We also thank the attendants to DySES (Dynamics of Socio Economic Systems) 2018 and Workshop on the Economic Science with Heterogeneous Interacting Agents 2019 for their very constructive comments.

Compliance with ethical standards

Conflict of interest

Both authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departimento di Matematica per le Scienze Economiche, Finanziarie e AttuarialiUniversità Cattolica del Sacro CuoreMilanItaly

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