Sampling biases in IP topology measurements

Abstract

Considerable attention has been focused on the properties of graphs derived from Internet measurements. Router-level topologies collected via traceroute studies have led some authors to conclude that the router graph of the Internet is a scale-free graph, or more generally a power-law random graph. In such a graph, the degree distribution of nodes follows a distribution with a power-law tail.In this paper we argue that the evidence to date for this conclusion is at best insufficient. We show that graphs appearing to have power-law degree distributions can arise surprisingly easily, when sampling graphs whose true degree distribution is not at all like a power-law. For example, given a classical Erdös-Rényi sparse, random graph, the subgraph formed by a collection of shortest paths from a small set of random sources to a larger set of random destinations can easily appear to show a degree distribution remarkably like a power-law.We explore the reasons for how this effect arises, and show that in such a setting, edges are sampled in a highly biased manner. This insight allows us to distinguish measurements taken from the Erdös-Rényi graphs from those taken from power-law random graphs. When we apply this distinction to a number of well-known datasets, we find that the evidence for sampling bias in these datasets is strong.£ Supported in part by NSF grants ANI-9986397, ANI-0095988, and ANI-0093296.

Describing and Simulating Internet Routes

“…Biases of graphs induced by acquisition through a small number of traceroute monitors have been studied for instance in by Lakhina et al [12]. However, recent studies by Dall'Asta et al [25] and Guillaume et al [14] show that one may be quite confident of the accuracy, using this kind of exploration, of distances and degrees, which are the main properties that we study here.…”

Quantifying the Importance of Vantage Points Distribution in Internet Topology Measurements

“…Figure 2 shows that vps with higher degree tend to have more agents (using degrees extracted from RouteViews produced the same results). This indicates that this is not a sampling bias caused by measurement artifact [16] but rather a hint that large ASes tend to "host" more agents. Additionally, vps with a single agent in them are mostly in the midlevel degrees section, and vps with more than one agent are scattered in a wide variety of degrees.…”

“…Lakhina et al [16] showed that AS degrees inferred using traceroute-like sampling technique, are highly affected by the location of the vps. The authors claimed that this bias could cause the observed power-law distribution, and suggested as a criteria for detecting bias in traceroute studies to check whether the highest-degree ASes tend to be near the measuring sources.…”

Adversarial topology discovery in network virtualization environments: a threat for ISPs?

“…Traditionally, much graph discovery research has been conducted in the context of today's complex networks such as the Internet which have fascinated scientists for many years, and there exists a wealth of results on the topic. One of the most influential measurement studies on the Internet topology was conducted by the Faloutsos brothers [12], and their work has subsequently been intensively discussed both in practical [17] and theoretical [2] papers. The classic instrument to discover Internet topologies is traceroute [7], but the tool has several problems which renders the problem challenging.…”