In this paper we introduce a framework for analyzing BGP connectivity, and evaluate a number of new complexity measures for a union of core backbone BGP tables. Sensitive to engineering resource limitations of router memory and CPU cycles, we focus on techniques to estimate redundancy of the merged tables, in particular how many entries are essential for complete and correct routing. We introduced the notion of policy atoms [BC01b] as part of a calculus in routing table analysis. We found that the number of atoms and individual counts of atoms with a given number of prefixes properly scale with the Internet’s growth and with filtering of prefixes by length. We show that the use of atoms can potentially reduce the number of route announcements by a factor of two, with all routing policies being preserved. Atoms thus represent Internet properties in an accurate way, yet with much smaller complexity. Several of our analysis results suggest that commonly held Internet engineering beliefs require re-consideration. We find that more specific routes had a relatively constant share of routes in backbone tables across 2000/2001. On the other hand, the churn of more specific routes was much larger than that of top prefixes. We also find that deaggregation of existing announcements is a second major source (beyond announcement of recently allocated address space) of new top (least specific) prefixes in global BGP tables. We also provide examples of misconfiguration and noise in BGP data, including multi-origin prefixes, AS paths with apparent routing loops (some of them due to typographical errors, other actual loops undetected by local BGP speakers), inadvertent transit through customer ASes.