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40
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 1407 (9 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.
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 87 (10 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.
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 81 (11 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.
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 66 (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.
A community based mobility model for ad hoc network research
 in Proceedings of ACM REALMAN
, 2006
"... Validation of mobile ad hoc network protocols relies almost exclusively on simulation. The value of the validation is, therefore, highly dependent on how realistic the movement models used in the simulations are. Since there is a very limited number of available real traces in the public domain, syn ..."
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Cited by 64 (7 self)
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Validation of mobile ad hoc network protocols relies almost exclusively on simulation. The value of the validation is, therefore, highly dependent on how realistic the movement models used in the simulations are. Since there is a very limited number of available real traces in the public domain, synthetic models for movement pattern generation must be used. However, most widely used models are currently very simplistic, their focus being ease of implementation rather than soundness of foundation. As a consequence, simulation results of protocols are often based on randomly generated movement patterns and, therefore, may differ considerably from those that can be obtained by deploying the system in real scenarios. Movement is strongly affected by the needs of humans to socialise or cooperate, in one form or another. Fortunately, humans are known to associate in particular ways that can be mathematically modelled and that have been studied in social sciences for years. In this paper we propose a new mobility model founded on social network theory. The model allows collections of hosts to be grouped together in a way that is based on social relationships among the individuals. This grouping is then mapped to a topographical space, with movements influenced by the strength of social ties that may also change in time. We have validated our model with real traces by showing that the synthetic mobility traces are a very good approximation of human movement patterns. We have also run simulations of AODV and DSR routing protocols on the mobility model and show how the message delivery ratio is affected by this type of mobility. 1.
Detecting richclub ordering in complex networks,” Arxiv preprint physics/0602134
, 2006
"... Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1, 2, 3, 4, 5]. The “richclub ..."
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Cited by 35 (0 self)
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Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1, 2, 3, 4, 5]. The “richclub” phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences [4, 5, 6]. Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the richclub phenomenon. The presented analysis enables the measurement of the richclub ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains 1.
Distributed Approaches to Triangulation and Embedding
 In Proceedings 16th ACMSIAM Symposium on Discrete Algorithms (SODA
, 2005
"... A number of recent papers in the networking community study the distance matrix defined by the nodetonode latencies in the Internet and, in particular, provide a number of quite successful distributed approaches that embed this distance into a lowdimensional Euclidean space. In such algorithms it ..."
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Cited by 30 (6 self)
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A number of recent papers in the networking community study the distance matrix defined by the nodetonode latencies in the Internet and, in particular, provide a number of quite successful distributed approaches that embed this distance into a lowdimensional Euclidean space. In such algorithms it is feasible to measure distances among only a linear or nearlinear number of node pairs; the rest of the distances are simply not available. Moreover, for applications it is desirable to spread the load evenly among the participating nodes. Indeed, several recent studies use this ’fully distributed ’ approach and achieve, empirically, a low distortion for all but a small fraction of node pairs. This is concurrent with the large body of theoretical work on metric embeddings, but there is a fundamental distinction: in the theoretical approaches to metric embeddings, full and centralized access to the distance matrix is assumed and heavily used. In this paper we present the first fully distributed embedding algorithm with provable distortion guarantees for doubling metrics (which have been proposed as a reasonable abstraction of Internet latencies), thus providing some insight into the empirical success of the recent Vivaldi algorithm [7]. The main ingredient of our embedding algorithm is an improved fully distributed algorithm for a more basic problem of triangulation, where the triangle inequality is used to infer the distances that have not been measured; this problem received a considerable attention in the networking community, and has also been studied theoretically in [19]. We use our techniques to extend ɛrelaxed embeddings and triangulations to infinite metrics and arbitrary measures, and to improve on the approximate distance labeling scheme of Talwar [36]. 1
Classes of complex networks defined by roletorole connectivity profiles
, 2007
"... In physical, biological, technological and social systems, interactions between units give rise to intricate networks. These—typically nontrivial—structures, in turn, critically affect the dynamics and properties of the system. The focus of most current research on complex networks is, still, on gl ..."
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Cited by 24 (1 self)
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In physical, biological, technological and social systems, interactions between units give rise to intricate networks. These—typically nontrivial—structures, in turn, critically affect the dynamics and properties of the system. The focus of most current research on complex networks is, still, on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most realworld networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes on the basis of their link type frequency. Importantly, we demonstrate that these structural features cannot be captured by means of often studied global properties.
Epidemic spreading in complex networks with degree correlations
 Proceedings of the XVIII Sitges Conference on Statistical Mechanics, Lecture Notes in Physics
, 2003
"... We review the behavior of epidemic spreading on complex networks in which there are explicit correlations among the degrees of connected vertices. 1 ..."
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Cited by 20 (1 self)
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We review the behavior of epidemic spreading on complex networks in which there are explicit correlations among the degrees of connected vertices. 1
Folks in Folksonomies: Social Link Prediction from Shared Metadata
"... Web 2.0 applications have attracted a considerable amount of attention because their openended nature allows users to create lightweight semantic scaffolding to organize and share content. To date, the interplay of the social and semantic components of social media has been only partially explored. ..."
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Cited by 20 (0 self)
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Web 2.0 applications have attracted a considerable amount of attention because their openended nature allows users to create lightweight semantic scaffolding to organize and share content. To date, the interplay of the social and semantic components of social media has been only partially explored. Here we focus on Flickr and Last.fm, two social media systems in which we can relate the tagging activity of the users with an explicit representation of their social network. We show that a substantial level of local lexical and topical alignment is observable among users who lie close to each other in the social network. We introduce a null model that preserves user activity while removing local correlations, allowing us to disentangle the actual local alignment between users from statistical effects due to the assortative mixing of user activity and centrality in the social network. This analysis suggests that users with