Network topology generators

Abstract

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.

Distances in random graphs with finite variance degrees

“…In a seminal paper [22], Faloutsos et al have shown that the degree distribution of autonomous systems in Internet follows a power law with power exponent τ ≈ 2.2. Thus, the power law random graph with this value of τ can possibly lead to a good Internet model on the autonomous systems (AS) level (see [22,38]). For the Internet on the more detailed router level, extensive measurements exist for the hopcount, which is the number of routers traversed between two typical routers, as well as for the AS-count, which is the number of autonomous systems traversed between two typical routers.…”

“…In [38], and inspired by the observed power law degree sequence in [22], the configuration model with i.i.d. degrees is proposed as a model for the AS-graph in Internet, and it is argued on a qualitative basis that this simple model serves as a better model for the Internet topology than currently used topology generators.…”

“…In computer science and electrical engineering, massive Internet measurements have lead to fundamental questions in the modelling and characterization of the Internet topology [22,38]. These modelling questions drive the understanding of the Internet's complex behavior and allow to plan and to control end-to-end communication.…”

Sampling large Internet topologies for simulation purposes

“…The generators either use ''biased'' or preferential growth policy [2,5,8,16,35] or force a power law degree distribution [1,24]. These constructive method produce synthetic graphs by focusing on matching their degree distributions with that of real Internet instances, and they often fail to match other topological properties, as multiply documented in [8,12,22,24,45].…”

Reducing Large Internet Topologies for Faster Simulations

“…The weakness of these constructive methods lies in their dependence on the principles of construction, and the choice of parameter values. Furthermore, several of them focus on matching the degree distribution, while they often fail to match other topological properties, as multiply documented [5] [7] [15] [16] [29].…”