  In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with
preferred degrees and presented simulation and analytic studies of a single,
homogeneous system as well as two interacting networks. Here, we extend these
studies to a wider range of parameter space, in a more systematic fashion.
Though the interaction we introduced seems simple and intuitive, it produced
dramatically different behavior in the single- and two-network systems.
Specifically, partitioning the single network into two identical sectors, we
find the cross-link distribution to be a sharply peaked Gaussian. In stark
contrast, we find a very broad and flat plateau in the case of two interacting
identical networks. A sound understanding of this phenomenon remains elusive.
Exploring more asymmetric interacting networks, we discover a kind of
`universal behavior' for systems in which the `introverts' (nodes with smaller
preferred degree) are far outnumbered. Remarkably, an approximation scheme for
their degree distribution can be formulated, leading to very successful
predictions.
