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Structure of complex networks: Quantifying edge-to-edge relations by failure-induced flow redistribution

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  • SCHAUB, MICHAEL T.
  • LEHMANN, JÖRG
  • YALIRAKI, SOPHIA N.
  • BARAHONA, MAURICIO

Abstract

The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is often focalized on edge processes, and a dual edge-centric perspective can often prove more natural. Here we present graph-theoretical measures to quantify edge-to-edge relations inspired by the notion of flow redistribution induced by edge failures. Our measures, which are related to the pseudo-inverse of the Laplacian of the network, are global and reveal the dynamical interplay between the edges of a network, including potentially non-local interactions. Our framework also allows us to define the embeddedness of an edge, a measure of how strongly an edge features in the weighted cuts of the network. We showcase the general applicability of our edge-centric framework through analyses of the Iberian power grid, traffic flow in road networks, and the C. elegans neuronal network.

Suggested Citation

  • Schaub, Michael T. & Lehmann, Jã–Rg & Yaliraki, Sophia N. & Barahona, Mauricio, 2014. "Structure of complex networks: Quantifying edge-to-edge relations by failure-induced flow redistribution," Network Science, Cambridge University Press, vol. 2(1), pages 66-89, April.
    • Handle: RePEc:cup:netsci:v:2:y:2014:i:01:p:66-89_00
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    Cited by:

    1. Singh, Priti & Chakraborty, Abhishek & Manoj, B.S., 2017. "Link Influence Entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 701-713.
    2. Dhruv Saxena & Alexis Arnaudon & Oscar Cipolato & Michele Gaio & Alain Quentel & Sophia Yaliraki & Dario Pisignano & Andrea Camposeo & Mauricio Barahona & Riccardo Sapienza, 2022. "Sensitivity and spectral control of network lasers," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    3. Jin, Yi & Zhang, Qingyuan & Chen, Yunxia & Lu, Zhendan & Zu, Tianpei, 2023. "Cascading failures modeling of electronic circuits with degradation using impedance network," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    4. Franz Kaiser & Philipp C. Böttcher & Henrik Ronellenfitsch & Vito Latora & Dirk Witthaut, 2022. "Dual communities in spatial networks," Nature Communications, Nature, vol. 13(1), pages 1-12, December.

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