  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.
