Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Physics and Astronomy

First Advisor

Beate Schmittmann

Second Advisor

Royce Zia


Many specific networks (e.g., internet, power grid, interstates), have been characterized well, but in isolation from one another. Yet, in the real world, different networks support each other's functions, and so far, little is known about how their interactions affect their structure 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 profound effect. In certain regime of parameter space, mean-field approximations provide good insight into observed behaviors. Third, reminiscent of introverts and extroverts in a population, we consider an extreme limit of our two-network model. Using a self-consistent mean-field approximation, we are able to predict 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 present results for models involving several other forms of interaction.


Copyright Owner

Wenjia Liu



File Format


File Size

112 pages

Included in

Physics Commons