Many specific networks (e.g., Internet, control grid, interstates) have been characterized well but in segregation from a different one. Yet, in the actual world, diverse networks bear each other’s functions, and so far, little is identified in relation to how their relations affect their organization and functionality. To address this issue, we introduce a stochastically evolving network, namely a preferred degree network, and study the interactions between such two networks. First, a homogeneous preferred degree network is studied. The resultant degree distribution is consistent with a Laplacian distribution, and an approximate theory provides good explanations. Second, another preferred degree network is introduced and coupled to the first following some specific rules. When the interaction is present, this system exhibits both interesting and puzzling features. Generalizing the theory for the homogeneous network, we are able to explain the total degree distributions well, but not the intra- or inter-group degree distributions. To develop a better understanding, we perform a systematic study of the number of inter-group links. We find that the interactions between networks have a weighty effect. In certain regime of parameter space, mean-field approximations provide good insight into observed behaviors. Third, redolent of introverts and extroverts in a population, we consider an extreme limit of our two-network model. Using a self-consistent mean-field rough calculation, we are able to foretell its degree distributions. Monitoring the total number of inter-group links between the two communities, we find an unusual transition, and succeed in predicting its key features. Finally, we at hand results for models involving quite a few other forms of interaction.

dynamic network, adaptive network.