The connectivity of the autonomous systems (ASs) in the Internet
can be modeled as a time-evolving random graph, whose nodes
represent ASs (or routers), and whose edges represent direct connections between them. Even though this graph has some random aspects, its properties show it
to be fundamentally different from "traditional'' random graphs.
In the first part of this paper, we use real BGP data to study
some properties of the AS connectivity graph and its evolution in
time. In the second part, we build a simple model that is inspired
by observations made in the first part, and we discuss simulations
of this model.