  Two stochastic models are proposed to generate a system composed of two
interdependent scale-free (SF) or Erd\H{o}s-R\'{e}nyi (ER) networks where
interdependent nodes are connected with exponential or power-law relation, as
well as different dependence strength, respectively. Each subnetwork grows
through the addition of new nodes with constant accelerating random attachment
in the first model but with preferential attachment in the second model. Two
subnetworks interact with multi-support and undirectional dependence links. The
effect of dependence relations and strength between subnetworks are analyzed in
the percolation behavior of fully interdependent networks against random
failure, both theoretically and numerically, and as a result, for both
relations: interdependent SF networks show a second-order percolation phase
transition and increased dependence strength decreases the robustness of the
system, whereas, interdependent ER networks show the opposite results. In
addition, power-law relation between networks yields greater robustness than
exponential one at given dependence strength.
