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97
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 2079 (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.
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 356 (3 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 173 (40 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
Gossipbased Peer Sampling
, 2007
"... Gossipbased communication protocols are appealing in largescale distributed applications such as information dissemination, aggregation, and overlay topology management. This paper factors out a fundamental mechanism at the heart of all these protocols: the peersampling service. In short, this se ..."
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Cited by 140 (40 self)
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Gossipbased communication protocols are appealing in largescale distributed applications such as information dissemination, aggregation, and overlay topology management. This paper factors out a fundamental mechanism at the heart of all these protocols: the peersampling service. In short, this service provides every node with peers to gossip with. We promote this service to the level of a firstclass abstraction of a largescale distributed system, similar to a name service being a firstclass abstraction of a localarea system. We present a generic framework to implement a peersampling service in a decentralized manner by constructing and maintaining dynamic unstructured overlays through gossiping membership information itself. Our framework generalizes existing approaches and makes it easy to discover new ones. We use this framework to empirically explore and compare several implementations of the peersampling service. Through extensive simulation experiments we show that—although all protocols provide a good quality uniform random stream of peers to each node locally—traditional theoretical assumptions about the randomness of the unstructured overlays as a whole do not hold in any of the instances. We also show that different design decisions result in severe differences from the point of view of two crucial aspects: load balancing and fault tolerance. Our simulations are validated by means of a widearea implementation.
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 124 (20 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&quot;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 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 112 (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.
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 70 (10 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
Complex networks: smallworld, scalefree and beyond
 IEEE Circuits Syst. Mag
, 2003
"... Abstract: In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this eme ..."
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Cited by 64 (6 self)
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Abstract: In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this emerging and active field of research. The present article reviews some basic concepts, important progress, and significant results in the current studies of various complex networks, with emphasis on the relationship between the topology and the dynamics of such complex networks. Some fundamental properties and typical complex network models are described, and as an example the epidemic dynamics are analyzed and discussed in some detail. Finally, the important issue of robustness versus fragility of dynamical synchronization in complex networks is introduced and discussed. Index terms – complex network, smallworld network, scalefree network, synchronization, robustness
Epidemics and immunization in scalefree networks
 IN: BORNHOLDT S, AND SCHUSTER H G (EDS.) HANDBOOK OF GRAPH AND NETWORKS
, 2003
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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 29 (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.