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147
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.
A FirstPrinciples Approach to Understanding the Internet's Routerlevel Topology
, 2004
"... A detailed understanding of the many facets of the Internet's topological structure is critical for evaluating the performance of networking protocols, for assessing the effectiveness of proposed techniques to protect the network from nefarious intrusions and attacks, or for developing improved ..."
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Cited by 213 (19 self)
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A detailed understanding of the many facets of the Internet's topological structure is critical for evaluating the performance of networking protocols, for assessing the effectiveness of proposed techniques to protect the network from nefarious intrusions and attacks, or for developing improved designs for resource provisioning. Previous studies of topology have focused on interpreting measurements or on phenomenological descriptions and evaluation of graphtheoretic properties of topology generators. We propose a complementary approach of combining a more subtle use of statistics and graph theory with a firstprinciples theory of routerlevel topology that reflects practical constraints and tradeoffs. While there is an inevitable tradeoff between model complexity and fidelity, a challenge is to distill from the seemingly endless list of potentially relevant technological and economic issues the features that are most essential to a solid understanding of the intrinsic fundamentals of network topology. We claim that very simple models that incorporate hard technological constraints on router and link bandwidth and connectivity, together with abstract models of user demand and network performance, can successfully address this challenge and further resolve much of the confusion and controversy that has surrounded topology generation and evaluation.
Towards Capturing Representative ASLevel Internet Topologies
 Computer Networks Journal
, 2002
"... Recent studies concerning the Internet connectivity at the AS level have attracted considerable attention. These studies have exclusively relied on the BGP data from Oregon routeviews [1] to derive some unexpected and intriguing results. The Oregon routeviews data sets reflect AS peering relations ..."
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Cited by 175 (23 self)
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Recent studies concerning the Internet connectivity at the AS level have attracted considerable attention. These studies have exclusively relied on the BGP data from Oregon routeviews [1] to derive some unexpected and intriguing results. The Oregon routeviews data sets reflect AS peering relationships, as reported by BGP, seen from a handful of vantage points in the global Internet. The possibility that these data sets from Oregon routeviews may provide only a very sketchy picture of the complete interAS connections that exist in the actual Internet has received surprisingly little scrutiny. In this paper, we will use the term "AS peering relationship" to mean that there is "at least one direct routerlevel connection" between two existing ASs, and that these two ASs agree to exchange traffic by enabling BGP between them. By augmenting the Oregon routeviews data sets with BGP summary information from a large number of Internet Looking Glass sites and with routing policy information from Internet Routing Registry (IRR) databases, we find that (1) a significant number of existing AS connections remain hidden from most BGP routing tables, (2) the AS connections to tier1 ASs are in general more easily observed than those to non tier1 ASs, and (3) there are at least about 2550% more AS connections in the Internet than commonlyused BGPderived AS maps reveal (but only about 2% more ASs). These findings point out the need for an increased awareness of and a more critical attitude toward the applicability and completeness of given data sets at hand when establishing the generality of any particular observations about the Internet.
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.
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.
ConstraintBased Geolocation of Internet Hosts
, 2004
"... Geolocation of Internet hosts enables a diverse and interesting new class of locationaware applications. Previous measurementbased approaches use reference hosts, called landmarks, with a wellknown geographic location to provide the location estimation of a target host. This leads to a discrete s ..."
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Cited by 93 (7 self)
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Geolocation of Internet hosts enables a diverse and interesting new class of locationaware applications. Previous measurementbased approaches use reference hosts, called landmarks, with a wellknown geographic location to provide the location estimation of a target host. This leads to a discrete space of answers, limiting the number of possible location estimates to the number of adopted landmarks. In contrast, we propose ConstraintBased Geolocation (CBG), which infers the geographic location of Internet hosts using multilateration with distance constraints, thus establishing a continuous space of answers instead of a discrete one. CBG accurately transforms delay measurements to geographic distance constraints, and then uses multilateration to infer the geolocation of the target host. Our experimental results show that CBG outperforms the previous measurementbased geolocation techniques. Moreover, in contrast to previous approaches, our method is able to assign a confidence region to each given location estimate. This allows a locationaware application to assess whether the location estimate is sufficiently accurate for its needs.
Spatial networks
 PHYSICS REPORTS
, 2010
"... Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topolo ..."
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Cited by 93 (5 self)
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Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topology alone does not contain all the information. Characterizing and understanding
On the geographic location of internet resources
 IEEE Journal on Selected Areas in Communications
, 2003
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 67 (4 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Ten years in the evolution of the Internet ecosystem
 In ACM SIGCOMM IMC
, 2008
"... Our goal is to understand the evolution of the Autonomous System (AS) ecosystem over the last decade. Instead of focusing on abstract topological properties, we classify ASes into a number of “species ” depending on their function and business type. Further, we consider the semantics of interAS lin ..."
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Cited by 62 (11 self)
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Our goal is to understand the evolution of the Autonomous System (AS) ecosystem over the last decade. Instead of focusing on abstract topological properties, we classify ASes into a number of “species ” depending on their function and business type. Further, we consider the semantics of interAS links, in terms of customerprovider versus peering relations. We find that the available historic datasets from RouteViews and RIPE are not sufficient to infer the evolution of peering links, and so we restrict our focus to customerprovider links. Our findings highlight some important trends in the evolution of the Internet over the last decade, and hint at what the Internet is heading towards. After an exponential increase phase until 2001, the Internet now grows linearly in terms of both ASes and interAS links. The growth is mostly due to enterprise networks and content/access providers at the periphery of the Internet. The average path length remains almost constant mostly due to the increasing multihoming degree of transit and content/access providers. In recent years, enterprise networks prefer to connect to small transit providers, while content/access providers connect equally to both large and small transit providers. The AS species differ significantly from each other with respect to their rewiring activity; content/access providers are the most active. A few large transit providers act as “attractors ” or “repellers ” of customers. For many providers, strong attractiveness precedes strong repulsiveness by 39 months. Finally, in terms of regional growth, we find that the AS ecosystem is now larger and more dynamic in Europe than
Dependent rounding and its applications to approximation algorithms
 JOURNAL OF THE ACM
, 2006
"... We develop a new randomized rounding approach for fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: ffl low congestion multipath rout ..."
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Cited by 61 (8 self)
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We develop a new randomized rounding approach for fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: ffl low congestion multipath routing; ffl richer randomgraph models for graphs with a given degreesequence; ffl improved approximation algorithms for: (i) throughputmaximization in broadcast scheduling, (ii) delayminimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and