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Percolation in real interdependent networks

Nature Physics volume 11, pages 597–602 (2015)Cite this article

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Abstract

The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Whereas theoretical methods of direct applicability to real isolated networks exist, the frameworks developed so far in percolation theory for interdependent network layers are of little help in practical contexts, as they are suited only for special models in the limit of infinite size. Here, we introduce a set of heuristic equations that takes as inputs the adjacency matrices of the layers to draw the entire phase diagram for the interconnected network. We demonstrate that percolation transitions in interdependent networks can be understood by decomposing these systems into uncoupled graphs: the intersection among the layers, and the remainders of the layers. When the intersection dominates the remainders, an interconnected network undergoes a smooth percolation transition. Conversely, if the intersection is dominated by the contribution of the remainders, the transition becomes abrupt even in small networks. We provide examples of real systems that have developed interdependent networks sharing cores of ‘high quality’ edges to prevent catastrophic failures.

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Figure 1: Decomposition of interconnected networks into uncoupled graphs.
Figure 2: Percolation transition in artificial interconnected networks.
Figure 3: Percolation transition in interdependent biological networks.
Figure 4: Percolation transition in interconnected transportation networks.

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Acknowledgements

The author thanks C. Castellano and A. Flammini for comments and suggestions.

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  1. Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, Indiana 47408, USA

    Filippo Radicchi

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  1. Filippo Radicchi
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Correspondence to Filippo Radicchi.

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Radicchi, F. Percolation in real interdependent networks. Nature Phys 11, 597–602 (2015). https://doi.org/10.1038/nphys3374

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