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87
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.
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
A Geometric Preferential Attachment Model of Networks
 In Algorithms and Models for the WebGraph: Third International Workshop, WAW 2004
, 2004
"... We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with powerlaw degree distribution where the expansion property depends on a tunable parameter of the model. The vertices of Gn are n sequentially generat ..."
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Cited by 56 (4 self)
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We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with powerlaw degree distribution where the expansion property depends on a tunable parameter of the model. The vertices of Gn are n sequentially generated points x1, x2,..., xn chosen uniformly at random from the unit sphere in R 3. After generating xt, we randomly connect it to m points from those points in x1, x2,..., xt−1. 1
PageRank, HITS and a Unified Framework for Link Analysis
"... Two popular webpage ranking algorithms are HITS and PageRank. HITS emphasizes mutual reinforcement between authority and hub webpages, while PageRank emphasizes hyperlink weight normalization and web surfing based on random walk models. We systematically generalize/combine these concepts into a unif ..."
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Cited by 52 (4 self)
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Two popular webpage ranking algorithms are HITS and PageRank. HITS emphasizes mutual reinforcement between authority and hub webpages, while PageRank emphasizes hyperlink weight normalization and web surfing based on random walk models. We systematically generalize/combine these concepts into a unified framework. The ranking framework contains a large algorithm space; HITS and PageRank are two extreme ends in this space. We study several normalized ranking algorithms which are intermediate between HITS and PageRank, and obtain closedform solutions. We show that, to first order approximation, all ranking algorithms in this framework, including PageRank and HITS, lead to same ranking which is highly correlated with ranking by indegree.
A social hypertext model for finding community
 in blogs. Conference on Hypertext and Hypermedia
, 2006
"... Blogging has become the newest communication medium for creating a virtual community, a set of blogs linking back and forth to one another’s postings, while discussing common topics. In this paper, we examine how communities can be discovered through interconnected blogs as a form of social hypertex ..."
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Cited by 33 (1 self)
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Blogging has become the newest communication medium for creating a virtual community, a set of blogs linking back and forth to one another’s postings, while discussing common topics. In this paper, we examine how communities can be discovered through interconnected blogs as a form of social hypertext [14]. We propose a method and model that detects structures of community in the social network of blogs by integrating McMillan and Chavis ’ sense of community [26] along with network analysis [8, 11]. From the model, we measure community in the blogs by aligning centrality measures from social network analysis [17] with measures of sense of community obtained using behavioural surveys. We then illustrate the use of this approach with a case study built around an independent music blog. The strength of community measures were found to be well aligned with the network structure, based on centrality measures. Even though the sample size from the case study was small, once the structure and measure of communities are calibrated according to our social hypertext model, communities can be automatically found and measured for other blogs without the need for behavioural surveys.
Modeling trust and influence in the blogosphere using link polarity
 IN PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON WEBLOGS AND SOCIAL MEDIA (ICWSM
, 2007
"... There is a growing interest in social network analysis to explore how communities and individuals spread influence. We describe techniques to find "like minded" blogs based on blogtoblog link sentiment for a particular domain. Using simple sentiment detection techniques, we identify the ..."
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Cited by 29 (6 self)
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There is a growing interest in social network analysis to explore how communities and individuals spread influence. We describe techniques to find "like minded" blogs based on blogtoblog link sentiment for a particular domain. Using simple sentiment detection techniques, we identify the polarity (positive, negative or neutral) of the text surrounding links that point from one blog post to another. We use trust propagation models to spread this sentiment from a subset of connected blogs to other blogs and deduce likeminded blogs in the blog graph. Our techniques demonstrate the potential of using polar links for more generic problems such as detecting trustworthy nodes in web graphs.
Partitioning of Web Graphs by Community Topology
, 2005
"... We introduce a stricter Web community definition to overcome boundary ambiguity of a Web community defined by Flake, Lawrence and Giles [2], and consider the problem of finding communities that satisfy our definition. We discuss how to find such communities and hardness of this problem. We also prop ..."
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Cited by 29 (0 self)
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We introduce a stricter Web community definition to overcome boundary ambiguity of a Web community defined by Flake, Lawrence and Giles [2], and consider the problem of finding communities that satisfy our definition. We discuss how to find such communities and hardness of this problem. We also propose Web page partitioning by equivalence relation defined using the class of communities of our definition. Though the problem of e#ciently finding all communities of our definition is NPcomplete, we propose an e#cient method of finding a subclass of communities among the sets partitioned by each of n 1 cuts represented by a GomoryHu tree [10], and partitioning a Web graph by equivalence relation defined using the subclass.
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 28 (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
Finding Patterns in Blog Shapes and Blog Evolution
 ICWSM
, 2007
"... Can we cluster blogs into types by considering their typical posting and linking behavior? How do blogs evolve over time? In this work we answer these questions, by providing several sets of blog and post features that can help distinguish between blogs. The first two sets of features focus on the t ..."
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Cited by 20 (5 self)
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Can we cluster blogs into types by considering their typical posting and linking behavior? How do blogs evolve over time? In this work we answer these questions, by providing several sets of blog and post features that can help distinguish between blogs. The first two sets of features focus on the topology of the cascades that the blogs are involved in, and the last set of features focuses on the temporal evolution, using chaotic and fractal ideas. We also propose to use PCA to reduce dimensionality, so that we can visualize the resulting clouds of points. We run all our proposed tools on the icwsm dataset. Our findings are that (a) topology features can help us distinguish blogs, like ‘humor’ versus ‘conservative’ blogs (b) the temporal activity of blogs is very nonuniform and bursty but (c) surprisingly often, it is selfsimilar and thus can be compactly characterized by the socalled bias factor (the ‘80’ in a recursive 8020 distribution). Keywords social network analysis, principal component analysis, bursty behavior