Distinct channels of interaction in a complex networked system define networklayers, which co-exist and co-operate for the system's function. Towardsrealistic modeling and understanding such multiplex systems, we introduce andstudy a class of growing multiplex network models in which different networklayers coevolve, and examine how the entangled growth of coevolving layers canshape the overall network structure. We show analytically and numerically thatthe coevolution can induce strong degree correlations across layers, as well asmodulate degree distributions. We further show that such a coevolution-inducedcorrelated multiplexity can alter the system's response to dynamical process,exemplified by the suppressed susceptibility to a threshold cascade process.
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