Dynamics of degree distributions of social networks

Social network models aim to capture the complex structure of social connections. They are a framework for the design of control algorithms that take into account relationships, interactions, and communications between social actors. Based on three formation mechanisms - random attachment, triad formation, and network response - our work characterizes the dynamics of the degree distributions of social networks. In particular, we show that the complementary cumulative in- and out-degree distributions of highly clustered, reciprocal networks can be approximated by infinite dimensional time-varying linear systems. Furthermore, we determine the invariance of both limit distributions and the stability properties of the average degree.