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In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks withpreferred degrees and presented simulation and analytic studies of a single,homogeneous system as well as two interacting networks. Here, we extend thesestudies to a wider range of parameter space, in a more systematic fashion.Though the interaction we introduced seems simple and intuitive, it produceddramatically different behavior in the single- and two-network systems.Specifically, partitioning the single network into two identical sectors, wefind the cross-link distribution to be a sharply peaked Gaussian. In starkcontrast, we find a very broad and flat plateau in the case of two interactingidentical 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 smallerpreferred degree) are far outnumbered. Remarkably, an approximation scheme fortheir degree distribution can be formulated, leading to very successfulpredictions.

Modeling interacting dynamic networks: II. Systematic study of the statistical properties of cross-links between two networks with preferred degrees