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101
Dynamics of Large Networks
, 2008
"... A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models ..."
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Cited by 33 (0 self)
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A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models that explain processes which govern the network evolution, fit such models to real networks, and use them to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: it can help us spot anomalous graphs and outliers, forecast future graph structure and run simulations of network evolution. Another important aspect of our research is the study of “local ” patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these blocks have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large persontoperson
On the Vulnerability of Large Graphs
"... Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k node ..."
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Cited by 26 (11 self)
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Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k nodes and (c) a fast algorithm to choose the best such k nodes. We answer all these three questions: we give the justification behind our choices, we show that they agree with intuition as well as recent results in immunology. Moreover, we propose NetShield, a fast and scalable algorithm. Finally, we give experiments on large real graphs, where NetShield achieves tremendous speed savings exceeding 7 orders of magnitude, against straightforward competitors. 1
Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks
"... Abstract—Given a network of whocontactswhom or wholinkstowhom, will a contagious virus/product/meme spread and ‘takeover ’ (cause an epidemic) or dieout quickly? What will change if nodes have partial, temporary or permanent immunity? The epidemic threshold is the minimum level of virulence to ..."
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Cited by 24 (12 self)
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Abstract—Given a network of whocontactswhom or wholinkstowhom, will a contagious virus/product/meme spread and ‘takeover ’ (cause an epidemic) or dieout quickly? What will change if nodes have partial, temporary or permanent immunity? The epidemic threshold is the minimum level of virulence to prevent a viral contagion from dying out quickly and determining it is a fundamental question in epidemiology and related areas. Most earlier work focuses either on special types of graphs or on specific epidemiological/cascade models. We are the first to show the G2threshold (twice generalized) theorem, which nicely decouples the effect of the topology and the virus model. Our result unifies and includes as special case older results and shows that the threshold depends on the first eigenvalue of the connectivity matrix, (a) for any graph and (b) for all propagation models in standard literature (more than 25, including H.I.V.) [20], [12]. Our discovery has broad implications for the vulnerability of real, complex networks, and numerous applications, including viral marketing, blog dynamics, influence propagation, easy answers to ‘whatif ’ questions, and simplified design and evaluation of immunization policies. We also demonstrate our result using extensive simulations on one of the biggest available socialcontact graphs containing more than 31 million interactions among more than 1 million people representing the city of Portland, Oregon, USA. I.
Maximizing the Spread of Cascades Using Network Design
"... We introduce a new optimization framework to maximize the expected spread of cascades in networks. Our model allows a rich set of actions that directly manipulate cascade dynamics by adding nodes or edges to the network. Our motivating application is one in spatial conservation planning, where a cas ..."
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Cited by 24 (11 self)
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We introduce a new optimization framework to maximize the expected spread of cascades in networks. Our model allows a rich set of actions that directly manipulate cascade dynamics by adding nodes or edges to the network. Our motivating application is one in spatial conservation planning, where a cascade models the dispersal of wild animals through a fragmented landscape. We propose a mixed integer programming (MIP) formulation that combines elements from network design and stochastic optimization. Our approach results in solutions with stochastic optimality guarantees and points to conservation strategies that are fundamentally different from naive approaches. 1
Virus Propagation on TimeVarying Networks: Theory and Immunization Algorithms
"... Abstract. Given a contact network that changes over time (say, day vs night connectivity), and the SIS (susceptible/infected/susceptible, flu like) virus propagation model, what can we say about its epidemic threshold? That is, can we determine when a small infection will “takeoff ” and create an e ..."
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Cited by 22 (8 self)
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Abstract. Given a contact network that changes over time (say, day vs night connectivity), and the SIS (susceptible/infected/susceptible, flu like) virus propagation model, what can we say about its epidemic threshold? That is, can we determine when a small infection will “takeoff ” and create an epidemic? Consequently then, which nodes should we immunize to prevent an epidemic? This is a very real problem, since, e.g. people have different connections during the day at work, and during the night at home. Static graphs have been studied for a long time, with numerous analytical results. Timeevolving networks are so hard to analyze, that most existing works are simulation studies [5]. Specifically, our contributions in this paper are: (a) we formulate the problem by approximating it by a Nonlinear Dynamical system (NLDS), (b) we derive the first closed formula for the epidemic threshold of timevarying graphs under the SIS model, and finally (c) we show the usefulness of our threshold by presenting efficient heuristics and evaluate the effectiveness of our methods on synthetic and real data like the MIT reality mining graphs. 1
Spotting Culprits in Epidemics: How many and Which ones
 in Proceedings of the 12th IEEE ICDM
, 2012
"... Abstract—Given a snapshot of a large graph, in which an infection has been spreading for some time, can we identify those nodes from which the infection started to spread? In other words, can we reliably tell who the culprits are? In this paper we answer this question affirmatively, and give an effi ..."
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Cited by 18 (6 self)
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Abstract—Given a snapshot of a large graph, in which an infection has been spreading for some time, can we identify those nodes from which the infection started to spread? In other words, can we reliably tell who the culprits are? In this paper we answer this question affirmatively, and give an efficient method called NETSLEUTH for the wellknown SusceptibleInfected virus propagation model. Essentially, we are after that set of seed nodes that best explain the given snapshot. We propose to employ the Minimum Description Length principle to identify the best set of seed nodes and virus propagation ripple, as the one by which we can most succinctly describe the infected graph. We give an highly efficient algorithm to identify likely sets of seed nodes given a snapshot. Then, given these seed nodes, we show we can optimize the virus propagation ripple in a principled way by maximizing likelihood. With all three combined, NETSLEUTH can automatically identify the correct number of seed nodes, as well as which nodes are the culprits. Experimentation on our method shows high accuracy in the detection of seed nodes, in addition to the correct automatic identification of their number. Moreover, we show NETSLEUTH scales linearly in the number of nodes of the graph. Keywordsculprits; epidemics; diffusion; seeds; I.
Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks
 in Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on. IEEE, 2013
"... Abstract—We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary contact network by distributing vaccination resources throughout the network. We analyze a networked version of the SusceptibleInfectedSusceptible (SIS) epidemic model when individuals in the n ..."
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Cited by 17 (4 self)
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Abstract—We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary contact network by distributing vaccination resources throughout the network. We analyze a networked version of the SusceptibleInfectedSusceptible (SIS) epidemic model when individuals in the network present different levels of susceptibility to the epidemic. In this context, controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding the optimal distribution of vaccines throughout the network to control the spread of an epidemic outbreak. We propose a convex framework to find costoptimal distribution of vaccination resources when different levels of vaccination are allowed. We also propose a greedy approach with quality guarantees for the case of allornothing vaccination. We illustrate our approaches with numerical simulations in a real social network. I.
What Stops Social Epidemics?
 SUBMITTED TO ICWSM11
, 2011
"... Theoretical progress in understanding the dynamics of spreading processes on graphs suggests the existence of an epidemic threshold below which no epidemics form and above which epidemics spread to a significant fraction of the graph. We have observed information cascades on the social media site Di ..."
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Cited by 16 (4 self)
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Theoretical progress in understanding the dynamics of spreading processes on graphs suggests the existence of an epidemic threshold below which no epidemics form and above which epidemics spread to a significant fraction of the graph. We have observed information cascades on the social media site Digg that spread fast enough for one initial spreader to infect hundreds of people, yet end up affecting only 0.1 % of the entire network. We demonstrate two complementary effects that limit the final size of cascades on Digg. First, because of the highly clustered structure of the Digg network, most people who are aware of a story have been exposed to it via multiple friends. This structure lowers the epidemic threshold while also slowing the overall growth of cascades. In addition, we find that the mechanism for social contagion on Digg deviates from standard social contagion models, like the independent cascade model, and this severely curtails the size of social epidemics on Digg. These findings underscore the fundamental difference between information spread and other contagion processes: despite multiple opportunities for infection within a social group, people are less likely to become spreaders of information with repeated exposure.
Activity driven modeling of time varying networks
, 1203
"... Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network form ..."
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Cited by 14 (2 self)
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Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a timeaggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents ’ interactions and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Within this framework, highly dynamical networks can be described analytically, allowing a quantitative discussion of the biases induced by the timeaggregated representations in the analysis of dynamical processes. Network modeling [1–6] has long drawn on the tradition of social network analysis and graph theory, with models ranging from the ErdösRényi model to Logit models, p*models, and Markov random graphs [7–11]. In the last decade, the class of growing network models, exemplified by the preferential attachment model, has been made widely popular