On generating Internet hierarchical topology

Abstract

Internet topology has been shown to have the following two properties: (1) the Internet is a hierarchical network; (2) Internet topology at the autonomous system (AS) level follows power law degree distribution. Current models have the following characteristics: (1) they explicitly focus on one of these two well-known properties, either hierarchical structure or power law degree distribution. (2) The models which aim at capturing power law degree distribution focus on the exponent, and thus the distribution of low-degree nodes has not been paid the attention it deserves. In view of this, we study the degree distribution of Internet hierarchical structure. In our study, we classify Internet AS level topology into hierarchical structure based on the logical relationship between ASs, which is widely adopted in the literature. We observe power law degree distribution in each tier (except tier 1) of the hierarchical structure, and this phenomenon persists as the Internet grows. Based on this observation, we propose a mechanism that can generate topologies conforming to both hierarchical structure and power law degree distribution. We derive the formulae of degree distribution for our mechanism. We also give special attention to the distribution of degree-one and degree-two nodes since they consist of a large portion of the Internet and their distribution deviates significantly from the power law.