  The availability of large scale streaming network data has reinforced the
ubiquity of power-law distributions in observations and enabled precision
measurements of the distribution parameters. The increased accuracy of these
measurements allows new underlying generative network models to be explored.
The preferential attachment model is a natural starting point for these models.
This work adds additional model components to account for observed phenomena in
the distributions. In this model, preferential attachment is supplemented to
provide a more accurate theoretical model of network traffic. Specifically, a
probabilistic complex network model is proposed using preferential attachment
as well as additional parameters to describe the newly observed prevalence of
leaves and unattached nodes. Example distributions from this model are
generated by considering random sampling of the networks created by the model
in such a way that replicates the current data collection methods.
