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541
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 2578 (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.
Information Diffusion through Blogspace
 In WWW ’04
, 2004
"... We study the dynamics of information propagation in environments of lowoverhead personal publishing, using a large collection of weblogs over time as our example domain. We characterize and model this collection at two levels. First, we present a macroscopic characterization of topic propagation th ..."
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Cited by 386 (5 self)
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We study the dynamics of information propagation in environments of lowoverhead personal publishing, using a large collection of weblogs over time as our example domain. We characterize and model this collection at two levels. First, we present a macroscopic characterization of topic propagation through our corpus, formalizing the notion of longrunning "chatter" topics consisting recursively of "spike" topics generated by outside world events, or more rarely, by resonances within the community. Second, we present a microscopic characterization of propagation from individual to individual, drawing on the theory of infectious diseases to model the flow. We propose, validate, and employ an algorithm to induce the underlying propagation network from a sequence of posts, and report on the results.
Analysis of Topological Characteristics of Huge Online Social Networking Services
 In Proceedings of the 16th international conference on World Wide Web (WWW’07
, 2007
"... Abstract — Social networking services are a fastgrowing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in reallife social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySp ..."
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Cited by 257 (6 self)
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Abstract — Social networking services are a fastgrowing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in reallife social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, each with more than 10 million users, respectively. We have access to complete data of Cyworld’s ilchon (friend) relationships and analyze its degree distribution, clustering property, degree correlation, and evolution over time. We also use Cyworld data to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace and orkut. Cyworld, the oldest of the three, demonstrates a changing scaling behavior over time in degree distribution. The latest Cyworld data’s degree distribution exhibits a multiscaling behavior, while those of MySpace and orkut have simple scaling behaviors with different exponents. Very interestingly, each of the two exponents corresponds to the different segments in Cyworld’s degree distribution. Certain online social networking services encourage online activities that cannot be easily copied in real life; we show that they deviate from closeknit online social networks which show a similar degree correlation pattern to reallife social networks. I.
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 257 (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.
RMAT: A recursive model for graph mining
 In Fourth SIAM International Conference on Data Mining (SDM’ 04
, 2004
"... How does a ‘normal ’ computer (or social) network look like? How can we spot ‘abnormal ’ subnetworks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal moneylaundering rings), forecasting, and simulations (“how will a computer ..."
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Cited by 244 (17 self)
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How does a ‘normal ’ computer (or social) network look like? How can we spot ‘abnormal ’ subnetworks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal moneylaundering rings), forecasting, and simulations (“how will a computer virus spread?”). The heart of the problem is finding the properties of real graphs that seem to persist over multiple disciplines. We list such “laws ” and, more importantly, we propose a simple, parsimonious model, the “recursive matrix ” (RMAT) model, which can quickly generate realistic graphs, capturing the essence of each graph in only a few parameters. Contrary to existing generators, our model can trivially generate weighted, directed and bipartite graphs; it subsumes the celebrated ErdősRényi model as a special case; it can match the power law behaviors, as well as the deviations from them (like the “winner does not take it all ” model of Pennock et al. [21]). We present results on multiple, large real graphs, where we show that our parameter fitting algorithm (AutoMATfast) fits them very well. 1
Computer Immunology
 Communications of the ACM
, 1996
"... Natural immune systems protect animals from dangerous foreign pathogens, including bacteria, viruses, parasites, and toxins. Their role in the body is analogous to that of computer security systems in computing. Although there are many differences between living organisms and computer systems, this ..."
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Cited by 225 (8 self)
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Natural immune systems protect animals from dangerous foreign pathogens, including bacteria, viruses, parasites, and toxins. Their role in the body is analogous to that of computer security systems in computing. Although there are many differences between living organisms and computer systems, this article argues that the similarities are compelling and could point the way to improved computer security. Improvements can be achieved by designing computer immune systems that have some of the important properties illustrated by natural immune systems. These include multilayered protection, highly distributed detection and memory systems, diversity of detection ability across individuals, inexact matching strategies, and sensitivity to most new foreign patterns. We first give an overview of how the immune system relates to computer security. We then illustrate these ideas with two examples.
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 212 (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.
The effect of network topology on the spread of epidemics
 IN IEEE INFOCOM
, 2005
"... Many network phenomena are well modeled as spreads of epidemics through a network. Prominent examples include the spread of worms and email viruses, and, more generally, faults. Many types of information dissemination can also be modeled as spreads of epidemics. In this paper we address the question ..."
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Cited by 212 (8 self)
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Many network phenomena are well modeled as spreads of epidemics through a network. Prominent examples include the spread of worms and email viruses, and, more generally, faults. Many types of information dissemination can also be modeled as spreads of epidemics. In this paper we address the question of what makes an epidemic either weak or potent. More precisely, we identify topological properties of the graph that determine the persistence of epidemics. In particular, we show that if the ratio of cure to infection rates is smaller than the spectral radius of the graph, then the mean epidemic lifetime is of order log n, where n is the number of nodes. Conversely, if this ratio is bigger than a generalization of the isoperimetric constant of the graph, then the mean epidemic lifetime is of order � Ò�, for a positive constant �. We apply these results to several network topologies including the hypercube, which is a representative connectivity graph for a distributed hash table, the complete graph, which is an important connectivity graph for BGP, and the power law graph, of which the ASlevel Internet graph is a prime example. We also study the star topology and the ErdősRényi graph as their epidemic spreading behaviors determine the spreading behavior of power law graphs.
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 159 (19 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.
Modeling the Internet’s largescale topology
 Proc. Natl. Acad. Sci
, 2002
"... Network generators that capture the Internet’s largescale topology are crucial for the development of efficient routing protocols and modeling Internet traffic 1,2,3. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect ..."
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Cited by 148 (0 self)
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Network generators that capture the Internet’s largescale topology are crucial for the development of efficient routing protocols and modeling Internet traffic 1,2,3. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet’s evolution. By combining several independent databases capturing the time evolution, topology and physical layout of the Internet, we identify the universal mechanisms that shape the Internet’s router and autonomous system level topology. We find that the physical layout of nodes form a fractal set 4,5, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently employed exponential laws 6,7. The universal parameters that we extract significantly restrict the class of potentially correct Internet models and indicate that the networks created by all available topology generators are fundamentally different from the current Internet. In the light of extensive evidence that Internet protocol performance is greatly