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164
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 216 (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.
Cascading behavior in large blog graphs
 In SDM
, 2007
"... How do blogs cite and influence each other? How do such links evolve? Does the popularity of old blog posts drop exponentially with time? These are some of the questions that we address in this work. Blogs (weblogs) have become an important medium of information because of their timely publication, ..."
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Cited by 132 (25 self)
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How do blogs cite and influence each other? How do such links evolve? Does the popularity of old blog posts drop exponentially with time? These are some of the questions that we address in this work. Blogs (weblogs) have become an important medium of information because of their timely publication, ease of use, and wide availability. In fact, they often make headlines, by discussing and discovering evidence about political events and facts. Often blogs link to one another, creating a publicly available record of how information and influence spreads through an underlying social network. Aggregating links from several blog posts creates a directed graph which we analyze to discover the patterns of information propagation in blogspace, and thereby understand the underlying social network. Here we report some surprising findings of the blog linking and information propagation structure, after we analyzed one of the largest available datasets, with 45, 000 blogs and ≈ 2.2 million blogpostings. Our analysis also sheds light on how rumors, viruses, and ideas propagate over social and computer networks.
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.
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 101 (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
On the spread of viruses on the internet
 In SODA
, 2005
"... We analyze the contact process on random graphs generated according to the preferential attachment scheme as a model for the spread of viruses in the Internet. We show that any virus with a positive rate of spread from a node to its neighbors has a nonvanishing chance of becoming epidemic. Quantita ..."
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Cited by 66 (6 self)
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We analyze the contact process on random graphs generated according to the preferential attachment scheme as a model for the spread of viruses in the Internet. We show that any virus with a positive rate of spread from a node to its neighbors has a nonvanishing chance of becoming epidemic. Quantitatively, we discover an interesting dichotomy: for a virus with effective spread rate λ, if the infection starts at a typical vertex, then it develops log(1/λ) into an epidemic with probability λ Θ ( log log(1/λ)), but on average the epidemic probability is λΘ(1). 1
Exploiting Availability Prediction in Distributed Systems
, 2006
"... Looselycoupled distributed systems have significant scale and cost advantages over more traditional architectures, but the availability of the nodes in these systems varies widely. Availability modeling is crucial for predicting permachine resource burdens and understanding emergent, systemwide p ..."
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Cited by 61 (2 self)
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Looselycoupled distributed systems have significant scale and cost advantages over more traditional architectures, but the availability of the nodes in these systems varies widely. Availability modeling is crucial for predicting permachine resource burdens and understanding emergent, systemwide phenomena. We present new techniques for predicting availability and test them using traces taken from three distributed systems. We then describe three applications of availability prediction. The first, availabilityguided replica placement, reduces object copying in a distributed data store while increasing data availability. The second shows how availability prediction can improve routing in delaytolerant networks. The third combines availability prediction with virus modeling to improve forecasts of global infection dynamics.
On the performance of internet worm scanning strategies
 Elsevier Journal of Performance Evaluation
, 2003
"... Abstract — In recent years, fast spreading worms have become one of the major threats to the security of the Internet. In order to defend against future worms, it is important to understand how worms propagate and how different scanning strategies affect their propagation. In this paper, we model an ..."
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Cited by 57 (12 self)
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Abstract — In recent years, fast spreading worms have become one of the major threats to the security of the Internet. In order to defend against future worms, it is important to understand how worms propagate and how different scanning strategies affect their propagation. In this paper, we model and analyze worm propagation under various scanning strategies, such as idealized scan, uniform scan, divideandconquer scan, local preference scan, sequential scan, target scan, etc. We also analyze and discuss how attackers could optimize their scanning strategies, and provide some guidelines for building up a monitoring infrastructure to defend against future worms. I.
Doulion: Counting Triangles in Massive Graphs with a Coin
 PROCEEDINGS OF ACM KDD,
, 2009
"... Counting the number of triangles in a graph is a beautiful algorithmic problem which has gained importance over the last years due to its significant role in complex network analysis. Metrics frequently computed such as the clustering coefficient and the transitivity ratio involve the execution of a ..."
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Cited by 53 (16 self)
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Counting the number of triangles in a graph is a beautiful algorithmic problem which has gained importance over the last years due to its significant role in complex network analysis. Metrics frequently computed such as the clustering coefficient and the transitivity ratio involve the execution of a triangle counting algorithm. Furthermore, several interesting graph mining applications rely on computing the number of triangles in the graph of interest. In this paper, we focus on the problem of counting triangles in a graph. We propose a practical method, out of which all triangle counting algorithms can potentially benefit. Using a straightforward triangle counting algorithm as a black box, we performed 166 experiments on realworld networks and on synthetic datasets as well, where we show that our method works with high accuracy, typically more than 99 % and gives significant speedups, resulting in even ≈ 130 times faster performance.
Protecting against network infections: A game theoretic perspective
 In INFOCOM 2009, IEEE
, 2009
"... Abstract — Security breaches and attacks are critical problems in today’s networking. A keypoint is that the security of each host depends not only on the protection strategies it chooses to adopt but also on those chosen by other hosts in the network. The spread of Internet worms and viruses is on ..."
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Cited by 44 (2 self)
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Abstract — Security breaches and attacks are critical problems in today’s networking. A keypoint is that the security of each host depends not only on the protection strategies it chooses to adopt but also on those chosen by other hosts in the network. The spread of Internet worms and viruses is only one example. This class of problems has two aspects. First, it deals with epidemic processes, and as such calls for the employment of epidemic theory. Second, the distributed and autonomous nature of decisionmaking in major classes of networks (e.g., P2P, adhoc, and most notably the Internet) call for the employment of game theoretical approaches. Accordingly, we propose a unified framework that combines the Nintertwined, SIS epidemic model with a noncooperative game model. We determine the existence of a Nash equilibrium of the respective game and characterize its properties. We show that its quality, in terms of overall network security, largely depends on the underlying topology. We then provide a bound on the level of system inefficiency due to the noncooperative behavior, namely, the “price of anarchy ” of the game. We observe that the price of anarchy may be prohibitively high, hence we propose a scheme for steering users towards socially efficient behavior. I.