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