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109
The structure and function of complex networks
 SIAM REVIEW
, 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
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Cited by 2600 (7 self)
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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
On Distinguishing between Internet Power Law Topology Generators
, 2002
"... Recent work has shown that the node degree in the WWW induced graph and the ASlevel Internet topology exhibit power laws. Since then several algorithms have been proposed to generate such power law graphs. In this paper we evaluate the effectiveness of these generators to generate representative AS ..."
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Cited by 256 (4 self)
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Recent work has shown that the node degree in the WWW induced graph and the ASlevel Internet topology exhibit power laws. Since then several algorithms have been proposed to generate such power law graphs. In this paper we evaluate the effectiveness of these generators to generate representative ASlevel topologies. Our conclusions are mixed. Although they (mostly) do a reasonable job at capturing the power law exponent, they do less well in capturing the clustering phenomena exhibited by the Internet topology. Based on these results we propose a variation of the recent incremental topology generator of [6] that is more successful at matching the power law exponent and the clustering behavior of the Internet. Last, we comment on the small world behavior of the Internet topology.
DIMES: Let the Internet measure itself
 Computer Communication Review
, 2005
"... Abstract — Today’s Internet maps, which are all collected from a small number of vantage points, are falling short of being accurate. We suggest here a paradigm shift for this task. DIMES is a distributed measurement infrastructure for the Internet that is based on the deployment of thousands of lig ..."
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Cited by 207 (33 self)
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Abstract — Today’s Internet maps, which are all collected from a small number of vantage points, are falling short of being accurate. We suggest here a paradigm shift for this task. DIMES is a distributed measurement infrastructure for the Internet that is based on the deployment of thousands of light weight measurement agents around the globe. We describe the rationale behind DIMES deployment, discuss its design tradeoffs and algorithmic challenges, and analyze the structure of the Internet as it seen with DIMES. I.
Inet3.0: Internet topology generator
, 2002
"... Abstract In this report we present version 3.0 of Inet, an Autonomous System (AS) level Internet topologygenerator. Our understanding of the Internet topology is quickly evolving, and thus, our understanding of how synthetic topologies should be generated is changing too. We document our analysis of ..."
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Cited by 168 (2 self)
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Abstract In this report we present version 3.0 of Inet, an Autonomous System (AS) level Internet topologygenerator. Our understanding of the Internet topology is quickly evolving, and thus, our understanding of how synthetic topologies should be generated is changing too. We document our analysis of Inet2.2, which highlighted two shortcomings in its topologies. Inet3.0 improves upon Inet2.2's two main weaknesses by creating topologies with more accurate degree distributions and minimum vertexcovers as compared to Internet topologies. We also examine numerous other metrics to show that Inet3.0 better approximates the actual Internet AS topology than does Inet2.2. Inet3.0's topologies stilldo not well represent the Internet in terms of maximum clique size and clustering coefficient. These related problems stress a need for a better understanding of Internet connectivity and will be addressedin future work.
Graph mining: laws, generators, and algorithms
 ACM COMPUT SURV (CSUR
, 2006
"... How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in ..."
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Cited by 132 (7 self)
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How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in realworld graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.
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.
Collecting the Internet ASlevel Topology
 ACM SIGCOMM Computer Communications Review (CCR
, 2005
"... At the interdomain level, the Internet topology can be represented by a graph with Autonomous Systems (ASes) as nodes and AS peerings as links. This ASlevel topology graph has been widely used in a variety of research efforts. Conventionally this topology graph is derived from routing tables colle ..."
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Cited by 107 (12 self)
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At the interdomain level, the Internet topology can be represented by a graph with Autonomous Systems (ASes) as nodes and AS peerings as links. This ASlevel topology graph has been widely used in a variety of research efforts. Conventionally this topology graph is derived from routing tables collected by RouteViews or RIPE RIS. In this work, we assemble the most complete ASlevel topology by extending the conventional method along two dimensions. First, in addition to using data from RouteViews and RIPE RIS, we also collect data from many other sources, including route servers, looking glasses, and routing registries. Second, in addition to using routing tables, we also accumulate topological information from routing updates over time. The resulting topology graph on a recent day contains 44 % more links and 3 % more nodes than that from using RouteViews routing tables alone. Our data collection and topology generation process have been automated, and we publish the latest topology on the web on a daily basis. 1.
On the bias of traceroute sampling: or, powerlaw degree distributions in regular graphs
 In ACM STOC
, 2005
"... Understanding the graph structure of the Internet is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining this graph structure can be a surprisingly difficult task, as edges cannot be explicitly queried. For instance, empiri ..."
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Cited by 80 (1 self)
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Understanding the graph structure of the Internet is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining this graph structure can be a surprisingly difficult task, as edges cannot be explicitly queried. For instance, empirical studies of the network of Internet Protocol (IP) addresses typically rely on indirect methods like traceroute to build what are approximately singlesource, alldestinations, shortestpath trees. These trees only sample a fraction of the network’s edges, and a recent paper by Lakhina et al. found empirically that the resulting sample is intrinsically biased. Further, in simulations, they observed that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is Poisson. In this paper, we study the bias of traceroute sampling mathematically and, for a very general class of underlying degree distributions, explicitly calculate the distribution that will be observed. As example applications of our machinery, we prove that traceroute sampling finds powerlaw degree distributions in both δregular and Poissondistributed random graphs. Thus, our work puts the observations of Lakhina et al. on a rigorous footing, and extends them to nearly arbitrary degree distributions.
To peer or not to peer: Modeling the evolution of the Internet’s ASlevel topology
 In INFOCOM
, 2006
"... Abstract — Internet connectivity at the AS level, defined in terms of pairwise logical peering relationships, is constantly evolving. This evolution is largely a response to economic, political, and technological changes that impact the way ASs conduct their business. We present a new framework for ..."
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Cited by 78 (3 self)
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Abstract — Internet connectivity at the AS level, defined in terms of pairwise logical peering relationships, is constantly evolving. This evolution is largely a response to economic, political, and technological changes that impact the way ASs conduct their business. We present a new framework for modeling this evolutionary process by identifying a set of criteria that ASs consider either in establishing a new peering relationship or in reassessing an existing relationship. The proposed framework is intended to capture key elements in the decision processes underlying the formation of these relationships. We present two decision processes that are executed by an AS, depending on its role in a given peering decision, as a customer or a peer of another AS. When acting as a peer, a key feature of the AS’s corresponding decision model is its reliance on realistic interAS traffic demands. To reflect the enormous heterogeneity among customer or peer ASs, our decision models are flexible enough to accommodate a wide range of ASspecific objectives. We demonstrate the potential of this new framework by considering different decision models in various realistic “what if ” experiment scenarios. We implement these decision models to generate and study the evolution of the resulting AS graphs over time, and compare them against observed historical evolutionary features of the Internet at the AS level. I.