Population size estimation and Internet link structure

Traceroute sampling is a common approach for exploring the autonomous system (AS) graph of the Internet. It provides samples of links between autonomous systems, but these links are not drawn uniformly at random from all possible links. Rather, the rules that each AS uses are idiosyncratic and emergent. Here, we are interested in using the data from traceroute sampling to estimate the degree distribution of the network, a quantity of common interest in network modeling more broadly. We link these ideas to the methodology of multiple-recapture estimation of the size of a closed population using log-linear models. We apply our approach to produce new estimates of the degree distribution of the AS graph, and to provide further evidence that the degree distribution does indeed have heavy tails.