Abstract:
The clustering attachment (CA) model proposed by Bagrow and Brockmann in 2013 may be used as an evolution tool for undirected random networks. A general definition of the CA model is introduced. Theoretical results are obtained for a new CA model that can be treated as the former’s limit in the case of the model parameters $\alpha\to0$ and $\epsilon = 0$. This study is focused on the triangle count of connected nodes at an evolution step $n$, an important characteristic of the network clustering considered in the literature. As is proved for the new model below, the total triangle count $\Delta n$ tends to infinity almost surely as $n\to\infty$ and the growth rate of $E\Delta_n$ at an evolution step $n\geqslant2$ is higher than the logarithmic one. Computer simulation is used to model sequences of triangle counts. The simulation is based on the generalized Pólya–Eggenberger urn model, a novel approach introduced here for the first time.
Fulltext:
PDF file (755 kB)
First page:
PDF file