  We study a system composed from two interdependent networks A and B, where a
fraction of the nodes in network A depends on the nodes of network B and a
fraction of the nodes in network B depends on the nodes of network A. Due to
the coupling between the networks when nodes in one network fail they cause
dependent nodes in the other network to also fail. This invokes an iterative
cascade of failures in both networks. When a critical fraction of nodes fail
the iterative process results in a percolation phase transition that completely
fragments both networks. We show both analytically and numerically that
reducing the coupling between the networks leads to a change from a first order
percolation phase transition to a second order percolation transition at a
critical point. The scaling of the percolation order parameter near the
critical point is characterized by the critical exponent beta=1.
