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207
PowerLaws and the ASlevel Internet Topology
 IEEE/ACM Transactions on Networking
, 2003
"... In this paper, we study and characterize the topology of the Internet at the Autonomous System level. First, we show that the topology can be described efficiently with powerlaws. The elegance and simplicity of the powerlaws provide a novel perspective into the seemingly uncontrolled Internet struc ..."
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Cited by 109 (11 self)
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In this paper, we study and characterize the topology of the Internet at the Autonomous System level. First, we show that the topology can be described efficiently with powerlaws. The elegance and simplicity of the powerlaws provide a novel perspective into the seemingly uncontrolled Internet structure. Second, we show that powerlaws appear consistently over the last 5 years. We also observe that the powerlaws hold even in the most recent and more complete topology [10] with correlation coefficient above 99% for the degree powerlaw. In addition, we study the evolution of the powerlaw exponents over the 5 year interval and observe a variation for the degree based powerlaw of less than 10%. Third, we provide relationships between the exponents and other topological metrics.
The Internet ASLevel Topology: Three Data Sources and One Definitive Metric
"... We calculate an extensive set of characteristics for Internet AS topologies extracted from the three data sources most frequently used by the research community: traceroutes, BGP, and WHOIS. We discover that traceroute and BGP topologies are similar to one another but differ substantially from the W ..."
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Cited by 108 (15 self)
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We calculate an extensive set of characteristics for Internet AS topologies extracted from the three data sources most frequently used by the research community: traceroutes, BGP, and WHOIS. We discover that traceroute and BGP topologies are similar to one another but differ substantially from the WHOIS topology. Among the widely considered metrics, we find that the joint degree distribution appears to fundamentally characterize Internet AS topologies as well as narrowly define values for other important metrics. We discuss the interplay between the specifics of the three data collection mechanisms and the resulting topology views. In particular, we show how the data collection peculiarities explain differences in the resulting joint degree distributions of the respective topologies. Finally, we release to the community the input topology datasets, along with the scripts and output of our calculations. This supplement should enable researchers to validate their models against real data and to make more informed selection of topology data sources for their specific needs.
Resisting Structural Reidentification in Anonymized Social Networks
, 2008
"... We identify privacy risks associated with releasing network data sets and provide an algorithm that mitigates those risks. A network consists of entities connected by links representing relations such as friendship, communication, or shared activity. Maintaining privacy when publishing networked dat ..."
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Cited by 105 (6 self)
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We identify privacy risks associated with releasing network data sets and provide an algorithm that mitigates those risks. A network consists of entities connected by links representing relations such as friendship, communication, or shared activity. Maintaining privacy when publishing networked data is uniquely challenging because an individual’s network context can be used to identify them even if other identifying information is removed. In this paper, we quantify the privacy risks associated with three classes of attacks on the privacy of individuals in networks, based on the knowledge used by the adversary. We show that the risks of these attacks vary greatly based on network structure and size. We propose a novel approach to anonymizing network data that models aggregate network structure and then allows samples to be drawn from that model. The approach guarantees anonymity for network entities while preserving the ability to estimate a wide variety of network measures with relatively little bias.
Systematic topology analysis and generation using degree correlations
 In SIGCOMM
"... Researchers have proposed a variety of metrics to measure important graph properties, for instance, in social, biological, and computer networks. Values for a particular graph metric may capture a graph’s resilience to failure or its routing efficiency. Knowledge of appropriate metric values may inf ..."
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Cited by 94 (7 self)
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Researchers have proposed a variety of metrics to measure important graph properties, for instance, in social, biological, and computer networks. Values for a particular graph metric may capture a graph’s resilience to failure or its routing efficiency. Knowledge of appropriate metric values may influence the engineering of future topologies, repair strategies in the face of failure, and understanding of fundamental properties of existing networks. Unfortunately, there are typically no algorithms to generate graphs matching one or more proposed metrics and there is little understanding of the relationships among individual metrics or their applicability to different settings. We present a new, systematic approach for analyzing network topologies. We first introduce the dKseries of probability distributions specifying all degree correlations within dsized subgraphs of a given graph G. Increasing values of d capture progressively more properties of G at the cost of more complex representation of the probability distribution. Using this series, we can quantitatively measure the distance between two graphs and construct random graphs that accurately reproduce virtually all metrics proposed in the literature. The nature of the dKseries implies that it will also capture any future metrics that may be proposed. Using our approach, we construct graphs for d =0, 1, 2, 3 and demonstrate that these graphs reproduce, with increasing accuracy, important properties of measured and modeled Internet topologies. We find that the d = 2 case is sufficient for most practical purposes, while d = 3 essentially reconstructs the Internet AS and routerlevel topologies exactly. We hope that a systematic method to analyze and synthesize topologies offers a significant improvement to the set of tools available to network topology and protocol researchers.
Jellyfish: A conceptual model for the AS internet topology
, 2004
"... Several novel concepts and tools have revolutionized our understanding of the Internet topology. Most of the existing efforts attempt to develop accurate analytical models. In this paper, our goal is to develop an effective conceptual model: a model that can be easily drawn by hand, while at the sam ..."
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Cited by 91 (7 self)
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Several novel concepts and tools have revolutionized our understanding of the Internet topology. Most of the existing efforts attempt to develop accurate analytical models. In this paper, our goal is to develop an effective conceptual model: a model that can be easily drawn by hand, while at the same time, it captures significant macroscopic properties. We build the foundation for our model with two thrusts: a) we identify new topological properties, and b) we provide metrics to quantify the topological importance of a node. We propose the jellyfish as a model for the interdomain Internet topology. We show that our model captures and represents the most significant topological properties. Furthermore, we observe that the jellyfish has lasting value: it describes the topology for more than six years.
Spectral Analysis of Internet Topologies
, 2003
"... We perform spectral analysis of the Internet topology at the AS level, by adapting the standard spectral filtering method of examining the eigenvectors corresponding to the largest eigenvalues of matrices related to the adjacency matrix of the topology. We observe that the method suggests clusters o ..."
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Cited by 86 (6 self)
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We perform spectral analysis of the Internet topology at the AS level, by adapting the standard spectral filtering method of examining the eigenvectors corresponding to the largest eigenvalues of matrices related to the adjacency matrix of the topology. We observe that the method suggests clusters of ASes with natural semantic proximity, such as geography or business interests. We examine how these clustering properties vary in the core and in the edge of the network, as well as across geographic areas, over time, and between real and synthetic data. We observe that these clustering properties may be suggestive of traffic patterns and thus have direct impact on the link stress of the network. Finally, we use the weights of the eigenvector corresponding to the first eigenvalue to obtain an alternative hierarchical ranking of the ASes.
Conductance and Congestion in Power Law Graphs
, 2003
"... It has been observed that the degrees of the topologies of several communication networks follow heavy tailed statistics. What is the impact of such heavy tailed statistics on the performance of basic communication tasks that a network is presumed to support? How does performance scale with the size ..."
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Cited by 69 (6 self)
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It has been observed that the degrees of the topologies of several communication networks follow heavy tailed statistics. What is the impact of such heavy tailed statistics on the performance of basic communication tasks that a network is presumed to support? How does performance scale with the size of the network? We study routing in families of sparse random graphs whose degrees follow heavy tailed distributions. Instantiations of such random graphs have been proposed as models for the topology of the Internet at the level of Autonomous Systems as well as at the level of routers. Let n be the number of nodes. Suppose that for each pair of nodes with degrees du and dv we have O(dudv ) units of demand. Thus the total demand is O(n ). We argue analytically and experimentally that in the considered random graph model such demand patterns can be routed so that the flow through each link is at most O . This is to be compared with a bound # that holds for arbitrary graphs. Similar results were previously known for sparse random regular graphs, a.k.a. "expander graphs." The significance is that Internetlike topologies, which grow in a dynamic, decentralized fashion and appear highly inhomogeneous, can support routing with performance characteristics comparable to those of their regular counterparts, at least under the assumption of uniform demand and capacities. Our proof uses approximation algorithms for multicommodity flow and establishes strong bounds of a generalization of "expansion," namely "conductance." Besides routing, our bounds on conductance have further implications, most notably on the gap between first and second eigenvalues of the stochastic normalization of the adjacency matrix of the graph.
Compact routing on Internetlike graphs
 In Proc. IEEE INFOCOM
, 2004
"... Abstract — The ThorupZwick (TZ) compact routing scheme is the first generic stretch3 routing scheme delivering a nearly optimal pernode memory upper bound. Using both direct analysis and simulation, we derive the stretch distribution of this routing scheme on Internetlike interdomain topologies. ..."
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Cited by 64 (7 self)
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Abstract — The ThorupZwick (TZ) compact routing scheme is the first generic stretch3 routing scheme delivering a nearly optimal pernode memory upper bound. Using both direct analysis and simulation, we derive the stretch distribution of this routing scheme on Internetlike interdomain topologies. By investigating the TZ scheme on random graphs with powerlaw node degree distributions, Pk � k −γ, we find that the average TZ stretch is quite low and virtually independent of γ. In particular, for the Internet interdomain graph with γ � 2.1, the average TZ stretch is around 1.1, with up to 70 % of all pairwise paths being stretch1 (shortest possible). As the network grows, the average stretch slowly decreases. The routing table is very small, too. It is well below its upper bounds, and its size is around 50 records for 10 4node networks. Furthermore, we find that both the average shortest path length (i.e. distance) d and width of the distance distribution σ observed in the real Internet interAS graph have values that are very close to the minimums of the average stretch in the d and σdirections. This leads us to the discovery of a unique critical point of the average TZ stretch as a function of d and σ. The Internet distance distribution is located in a close neighborhood of this point. This is remarkable given the fact that the Internet interdomain topology has evolved without any direct attention paid to properties of the stretch distribution. It suggests the average stretch function may be an indirect indicator of the optimization criteria influencing the Internet’s interdomain topology evolution.
The richclub phenomenon in the Internet topology
 IEEE Comm. Lett
"... Abstract—We show that the Internet topology at the autonomous system (AS) level has a richclub phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The richclub is a core tier that we measured using the richclub connect ..."
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Cited by 52 (11 self)
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Abstract—We show that the Internet topology at the autonomous system (AS) level has a richclub phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The richclub is a core tier that we measured using the richclub connectivity and the nodenode link distribution. We obtained this core tier without any heuristic assumption between the ASs. The richclub phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured richclub of the AS graph with networks obtained using the Barabási–Albert (BA) scalefree network model, the Fitness BA model and the Inet–3.0 model. Index Terms—Internet, modeling, networks, topology. I.
The Temporal and Topological Characteristics of BGP Path Changes
 IN PROCEEDINGS OF IEEE ICNP
, 2003
"... BGP has been deployed in Internet for more than a decade. However, the events that cause BGP topological changes are not well understood. Although large traces of routing updates seen in BGP operation are collected by RIPE RIS and University of Oregon RouteViews, previous work examines this data set ..."
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Cited by 44 (3 self)
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BGP has been deployed in Internet for more than a decade. However, the events that cause BGP topological changes are not well understood. Although large traces of routing updates seen in BGP operation are collected by RIPE RIS and University of Oregon RouteViews, previous work examines this data set as individual routing updates. This paper describes methods that group routing updates into events. Since one event (a policy change or peering failure) results in many update messages, we cluster updates both temporally and topologically (based on the path vector information). We propose a new approach to analyzing the update traces, classifying the topological impact of routing events, and approximating the distance to the the Autonomous System originating the event. Our analysis provides some insight into routing behavior: First, at least 45% path changes are caused by events on transit peerings. Second, a significant number (2337%) of path changes are transient, in that routing updates indicate temporary path changes, but they ultimately converge on a path that is identical from the previously stable path. These observations suggest that a content provider cannot guarantee endtoend routing stability based solely on its relationship with its immediate ISP, and that better detection of transient changes may improve routing stability.