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74
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.
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 251 (6 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.
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 178 (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.
Power laws, Pareto distributions and Zipf’s law
 Contemporary Physics
, 2005
"... When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, econ ..."
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Cited by 170 (0 self)
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When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people’s personal fortunes all appear to follow power laws. The origin of powerlaw behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of powerlaw forms and the theories proposed to explain them. I.
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.
SmallWorld FileSharing Communities
, 2003
"... Web caches, content distribution networks, peertopeer file sharing networks, distributed file systems, and data grids all have in common that they involve a community of users who generate requests for shared data. In each case, overall system performance can be improved significantly if we can fi ..."
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Cited by 68 (9 self)
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Web caches, content distribution networks, peertopeer file sharing networks, distributed file systems, and data grids all have in common that they involve a community of users who generate requests for shared data. In each case, overall system performance can be improved significantly if we can first identify and then exploit interesting structure within a community's access patterns. To this end, we propose a novel perspective on file sharing based on the study of the relationships that form among users based on the files in which they are interested. We propose a new structure that captures common user interests in datathe datasharing graph and justify its utility with studies on three datadistribution systems: a highenergy physics collaboration, the Web, and the Kazaa peertopeer network. We find smallworld patterns in the datasharing graphs of all three communities. We analyze these graphs and propose some probable causes for these emergent smallworld patterns. The significance of smallworld patterns is twofold: it provides a rigorous support to intuition and, perhaps most importantly, it suggests ways to design mechanisms that exploit these naturally emerging patterns.
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
Email Worm Modeling and Defense
, 2004
"... Email worms constitute one of the major Internet security problems. In this paper, we present an email worm model that accounts for the behaviors of email users by considering email checking time and the probability of opening email attachments. Email worms spread over a logical network defined by e ..."
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Cited by 36 (3 self)
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Email worms constitute one of the major Internet security problems. In this paper, we present an email worm model that accounts for the behaviors of email users by considering email checking time and the probability of opening email attachments. Email worms spread over a logical network defined by email address relationship, which plays an important role in determining the spreading dynamics of an email worm. Our observations suggest that the node degrees of an email network are heavytailed distributed. We compare email worm propagation on three topologies: power law, small world and random graph topologies; and then study how the topology affects immunization defense on email worms. The impact of the power law topology on the spread of email worms is mixed: email worms spread more quickly on a power law topology than on a small world topology or a random graph topology, but immunization defense is more effective on a power law topology than on the other two.
Effects of missing data in social networks
 Social Networks
, 2003
"... We perform sensitivity analyses to assess the impact of missing data on the structural properties of social networks. The social network is conceived of as being generated by a bipartite graph, in which actors are linked together via multiple interaction contexts or affiliations. We discuss three pr ..."
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Cited by 28 (1 self)
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We perform sensitivity analyses to assess the impact of missing data on the structural properties of social networks. The social network is conceived of as being generated by a bipartite graph, in which actors are linked together via multiple interaction contexts or affiliations. We discuss three principal missing data mechanisms: network boundary specification (noninclusion of actors or affiliations), survey nonresponse, and censoring by vertex degree (fixed choice design), examining their impact on the scientific collaboration network from the Los Alamos Eprint Archive as well as random bipartite graphs. The simulation results show that network boundary specification and fixed choice designs can dramatically alter estimates of networklevel statistics. The observed clustering and assortativity coefficients are overestimated via omission of affiliations or fixed choice thereof, and underestimated via actor nonresponse, which results in inflated measurement error. We also find that social networks with multiple interaction contexts may have certain interesting properties due to the presence of overlapping cliques. In particular, assortativity by degree does not necessarily improve network robustness to random omission of nodes as predicted by current theory.