Small-world characteristics of Internet topologies and implications on multicast scaling

Recent work has shown that the physical connectivity of the Internet exhibits small-world behavior. Characterizing such behavior is important not only for generating realistic Internet topology, but also for the proper evaluation of large-scale content delivery techniques. Along this line, this paper tries to explain how the small-world behavior arises in the Internet topologies and how it impacts the performance of multicast techniques. First, we attribute the small-world behavior to two possible causes—namely the variability of vertex degree and the preference for local connections for vertices. We have found that both factors contribute with different relative degrees to the small-world behavior of the autonomous system (AS) level and router level Internet topologies. For the AS level topology, we observe that the high variability of vertex degree is sufficient to cause the small-world behavior, but for the router level topology, the preference for local connectivity plays a more important role. Second, we propose better models to generate small-world Internet topologies. Our models incorporate both causes of small-world behavior, and generate graphs closely resemble real Internet graphs. Third, using simulation we demonstrate the importance of our work by studying the scaling behavior of multicast techniques. We show that multicast tree size largely depends on the network topology. If topology generators capture only the variability of vertex degree, they are likely to underestimate the benefit of multicast techniques.