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

Abstract

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.

Accepted by JSTAT

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• How does homophily shape the topology of a dynamic network?
• Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition
• Co-evolution of nodes and links: diversity driven coexistence in cyclic competition of three species
• Exact results for the extreme Thouless effect in a model of network dynamics
• Fluctuations and Correlations in a Model of Extreme Introverts and Extroverts