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62
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.
Evolution of networks
 Adv. Phys
, 2002
"... We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence rece ..."
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Cited by 268 (2 self)
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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scalefree and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks selforganize into scalefree structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems
The Peer Sampling Service: Experimental Evaluation of Unstructured GossipBased Implementations
 In Middleware ’04: Proceedings of the 5th ACM/IFIP/USENIX international conference on Middleware
, 2004
"... Abstract. In recent years, the gossipbased communication model in largescale distributed systems has become a general paradigm with important applications which include information dissemination, aggregation, overlay topology management and synchronization. At the heart of all of these protocols l ..."
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Cited by 143 (29 self)
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Abstract. In recent years, the gossipbased communication model in largescale distributed systems has become a general paradigm with important applications which include information dissemination, aggregation, overlay topology management and synchronization. At the heart of all of these protocols lies a fundamental distributed abstraction: the peer sampling service. In short, the aim of this service is to provide every node with peers to exchange information with. Analytical studies reveal a high reliability and efficiency of gossipbased protocols, under the (often implicit) assumption that the peers to send gossip messages to are selected uniformly at random from the set of all nodes. In practice—instead of requiring all nodes to know all the peer nodes so that a random sample could be drawn—a scalable and efficient way to implement the peer sampling service is by constructing and maintaining dynamic unstructured overlays through gossiping membership information itself. This paper presents a generic framework to implement reliable and efficient peer sampling services. The framework generalizes existing approaches and makes it easy to introduce new ones. We use this framework to explore and compare several implementations of our abstract scheme. Through extensive experimental analysis, we show that all of them lead to different peer sampling services none of which is uniformly random. This clearly renders traditional theoretical approaches invalid, when the underlying peer sampling service is based on a gossipbased scheme. Our observations also help explain important differences between design choices of peer sampling algorithms, and how these impact the reliability of the corresponding service. 1
Epidemic Spreading in Real Networks: An Eigenvalue Viewpoint
 In SRDS
, 2003
"... Abstract How will a virus propagate in a real network?Does an epidemic threshold exist for a finite powerlaw graph, or any finite graph? How long does ittake to disinfect a network given particular values of infection rate and virus death rate? We answer the first question by providing equations th ..."
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Cited by 77 (18 self)
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Abstract How will a virus propagate in a real network?Does an epidemic threshold exist for a finite powerlaw graph, or any finite graph? How long does ittake to disinfect a network given particular values of infection rate and virus death rate? We answer the first question by providing equations that accurately model virus propagation in any network including real and synthesized networkgraphs. We propose a general epidemic threshold condition that applies to arbitrary graphs: weprove that, under reasonable approximations, the epidemic threshold for a network is closely relatedto the largest eigenvalue of its adjacency matrix. Finally, for the last question, we show that infections tend to zero exponentially below the epidemic threshold. We show that our epidemic threshold modelsubsumes many known thresholds for specialcase graphs (e.g., Erd"osR'enyi, BA powerlaw, homogeneous); we show that the threshold tends to zero for infinite powerlaw graphs. Finally, we illustrate thepredictive power of our model with extensive experiments on real and synthesized graphs. We show thatour threshold condition holds for arbitrary graphs.
Graph mining: Laws, generators, and algorithms
 ACM COMPUTING SURVEYS
, 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 i ..."
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Cited by 70 (6 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.
Epidemic Thresholds in Real Networks
"... How will a virus propagate in a real network? How long does it take to disinfect a network given particular values of infection rate and virus death rate? What is the single best node to immunize? Answering these questions is essential for devising networkwide strategies to counter viruses. In addi ..."
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Cited by 37 (9 self)
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How will a virus propagate in a real network? How long does it take to disinfect a network given particular values of infection rate and virus death rate? What is the single best node to immunize? Answering these questions is essential for devising networkwide strategies to counter viruses. In addition, viral propagation is very similar in principle to the spread of rumors, information, and “fads, ” implying that the solutions for viral propagation would also offer insights into these other problem settings. We answer these questions by developing a nonlinear dynamical system (NLDS) that accurately models viral propagation in any arbitrary network, including real and synthesized network graphs. We propose a general epidemic threshold condition for the NLDS system: we prove that the epidemic threshold for a network is exactly the inverse of the largest eigenvalue of its adjacency matrix. Finally, we show that below the epidemic threshold, infections die out at an exponential rate. Our epidemic threshold model subsumes many known thresholds for specialcase graphs (e.g., Erdös–Rényi, BA powerlaw, homogeneous). We demonstrate the predictive power of our model with extensive experiments on real and synthesized graphs, and show that our threshold condition holds for arbitrary graphs. Finally, we show how to utilize our threshold condition for practical uses: It can dictate which nodes to immunize; it can assess the effects of a throttling
Epidemics and immunization in scalefree networks
 IN: BORNHOLDT S, AND SCHUSTER H G (EDS.) HANDBOOK OF GRAPH AND NETWORKS
, 2003
"... ..."
LikelihoodBased Inference for Stochastic Models of Sexual Network Formation
 Popul. Biol
, 2004
"... SexuallyTransmitted Diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insi ..."
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Cited by 22 (5 self)
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SexuallyTransmitted Diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insight focuses attention on the distribution of sexual activity level in a population. In this paper, we develop several stochastic process models for the f'ormation of sexual partnership networks. Using likelihoodbased model selection procedures, we assess the fit of the different models to three large distributions of sexual partner counts: (1) Rakai, Uganda, (2) Sweden, and (3) the USA. Five of' the six singlesex networks were fit best by the negative binomial model. The American women's network was best fit by a powerlaw model, the Yule. For most networks, several competing models fit approximately equally well. These results sug gest three conclusions: (1) no single unitary process clearly underlies the formation of these sexual networks, (2) behavioral heterogeneity plays an essential role in network structure, (3) substantial model uncertainty exists for sexual network degree distributions. Behavioral research focused on the mechanisms of partnership f'ormation will play an essential role in specifying the best model for empirical degree distributions. We discuss the limitations of inferences f'rom such data, and the utility of degreebased epidemiological models more generally.
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
Galstyan A. Analysis of Social Voting Patterns on Digg
 In WOSN
, 2008
"... The social Web is transforming the way information is created and distributed. Blog authoring tools enable users to publish content, while sites such as Digg and Del.icio.us are used to distribute content to a wider audience. With content fast becoming a commodity, interest in using social networks ..."
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Cited by 20 (4 self)
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The social Web is transforming the way information is created and distributed. Blog authoring tools enable users to publish content, while sites such as Digg and Del.icio.us are used to distribute content to a wider audience. With content fast becoming a commodity, interest in using social networks to promote and find content has grown, both on the side of content producers (viral marketing) and consumers (recommendation). Here we study the role of social networks in promoting content on Digg, a social news aggregator that allows users to submit links to and vote on news stories. Digg’s goal is to feature the most interesting stories on its front page, and it aggregates opinions of its many users to identify them. Like other social networking sites, Digg allows users to designate other users as “friends ” and see what stories they found interesting. We studied the spread of interest in news stories submitted to Digg in June 2006. Our results suggest that pattern of the spread of interest in a story on the network is indicative of how popular the story will become. Stories that spread mainly outside of the submitter’s neighborhood go on to be very popular, while stories that spread mainly through submitter’s social neighborhood prove not to be very popular. This effect is visible already in the early stages of voting, and one can make a prediction about the potential audience of a story simply by analyzing where the initial votes come from.