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Cavity-based robustness analysis of interdependent networks: Influences of intranetwork and internetwork degree-degree correlations

We develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree correlations inside and between the networks on the network robustness against targeted attacks and random failures. We show that the developed methodology is reduced to the well-known generating function formalism in the absence of degree-degree correlations. The validity of the developed methodology is confirmed by a comparison with the results of numerical experiments. Our analytical results imply that the robustness of the interdependent networks depends considerably on both the intra- and internetwork degree-degree correlations in the case of targeted attacks, whereas the significance of the degree-degree correlations is relatively low for random failures.