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Many interdependent, real-world infrastructures involve interconnections between different communities or cities. Here we study if and how the effects of such interconnections can be described as an external field for interdependent networks experiencing first-order percolation transitions. We find that the critical exponents $gamma$ and $delta$, related to the external field can also be defined for first-order transitions but that they have different values than those found for second-order transitions. Surprisingly, we find that both sets of different exponents can be found even within a single model of interdependent networks, depending on the dependency coupling strength. Specifically, the exponent $gamma$ in the first-order regime (high coupling) does not obey the fluctuation dissipation theorem, whereas in the continuous regime (for low coupling) it does. Nevertheless, in both cases they satisfy Widoms identity, $delta - 1 = gamma / beta$ which further supports the validity of their definitions. Our results provide physical intuition into the nature of the phase transition in interdependent networks and explain the underlying reasons for two distinct sets of exponents.
In this work we tackle a kinetic-like model of opinions dynamics in a networked population endued with a quenched plurality and polarization. Additionally, we consider pairwise interactions that are restrictive, which is modeled with a smooth bounded
In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in a form of an abrupt first order transition. When the fraction of initial failed nodes
Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the systems structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that
Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al cite{PAR10B}). For example, the coupl