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 equa-tions 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 infec-tions tend to zero exponentially below the epidemic threshold. We show that our epidemic threshold modelsubsumes many known thresholds for special-case graphs (e.g., Erd"os-R'enyi, BA power-law, homoge-neous); we show that the threshold tends to zero for infinite power-law 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.

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 closed-form 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.

We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with power-law 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

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 network-wide 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 special-case 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

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.

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 blog-to-blog 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 like-minded 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.

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 NP-complete, 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.

In this paper we address the problem of organizing hidden-Web databases. Given a heterogeneous set of Web forms that serve as entry points to hidden-Web databases, our goal is to cluster the forms according to the database domains to which they belong. We propose a new clustering approach that models Web forms as a set of hyperlinked objects and considers visible information in the form context— both within and in the neighborhood of forms—as the basis for similarity comparison. Since the clustering is performed over features that can be automatically extracted, the process is scalable. In addition, because it uses a rich set of metadata, our approach is able to handle a wide range of forms, including content-rich forms that contain multiple attributes, as well as simple keyword-based search interfaces. An experimental evaluation over real Web data shows that our strategy generates high-quality clusters—measured both in terms of entropy and F-measure. This indicates that our approach provides an effective and general solution to the problem of organizing hidden-Web databases. 1

Web spamming, the practice of introducing artificial text and links into web pages to a#ect the results of searches, has been recognized as a major problem for search engines. It is also a serious problem for users because they are not aware of it and they tend to confuse trusting the search engine with trusting the results of a search. In this paper, we first analyze the influence that web spam has on the evolution of the search engines and we identify the strong relationship of spamming methods to propagandistic techniques in society. Our analysis provides a foundation to understanding why spamming works and o#ers new insight on how to address it. In particular, it suggest that one could use anti-propagandistic techniques in the web to recognize spam. The second part of the paper demonstrates such a technique, called backwards propagation of distrust. In society, recognition of an untrustworthy message (in the opinion of a particular person or other social entity) is a reason for questioning the entities that recommend the message. Entities that are found to strongly support untrustworthy messages become untrustworthy themselves. So, social distrust is propagated backwards for a number of steps. Our algorithm simulates this social behavior on the web graph. In our algorithm, starting from an untrustworthy (according to the end user) site s, we examine its trust neighborhood, that is, the neighborhood of sites that link to s in a few steps. Evaluating the sites-members of the neighborhood we identify a biconnected component (BCCs) with a high percentage of untrustworthy sites. BCCs are formed when there are multiple paths to reach s, thus indicating a concerted e#ort to promote s. This is not the case when starting from a trustworthy site. Our tool explores thousands o...

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