Following the long-held belief that the Internet is hierarchical, the network topology generators most widely used by the Internet research community, Transit-Stub and Tiers, create networks with a deliberately hierarchical structure. However, in 1999 a seminal paper by Faloutsos et al. revealed that the Internet's degree distribution is a power-law. Because the degree distributions produced by the Transit-Stub and Tiers generators are not power-laws, the research community has largely dismissed them as inadequate and proposed new network generators that attempt to generate graphs with power-law degree distributions.Contrary to much of the current literature on network topology generators, this paper starts with the assumption that it is more important for network generators to accurately model the large-scale structure of the Internet (such as its hierarchical structure) than to faithfully imitate its local properties (such as the degree distribution). The purpose of this paper is to determine, using various topology metrics, which network generators better represent this large-scale structure. We find, much to our surprise, that network generators based on the degree distribution more accurately capture the large-scale structure of measured topologies. We then seek an explanation for this result by examining the nature of hierarchy in the Internet more closely; we find that degree-based generators produce a form of hierarchy that closely resembles the loosely hierarchical nature of the Internet.

One of the many benefits of multicast, when compared to traditional unicast, is that multicast reduces the overall network load. While the importance of multicast is beyond dispute, there have been surprisingly few attempts to quantify multicast's reduction in overall network load. The only substantial and quantitative effort we are aware of is that of Chuang and Sirbu [3]. They calculate the number of links L in a multicast delivery tree connecting a random source to m random and distinct network sites; extensive simulations over a range of networks suggest that L(m) ∝ m 0.8 . In this paper we examine the function L(m) in more detail and derive the asymptotic form for L(m) in k-ary trees. These results suggest one possible explanation for the universality of the Chuang-Sirbu scaling behavior.