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arXiv · 1404.1811

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

Wenjia Liu·B. Schmittmann·R. K. P. Zia
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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.

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Wenjia Liu, B. Schmittmann, R. K. P. Zia. 2014-04-07. Modeling interacting dynamic networks: II. Systematic study of the statistical properties of cross-links between two networks with preferred degrees. https://doi.org/10.1088/1742-5468%2F2014%2F05%2Fp05021

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