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Link Analysis has been a popular and widely used Web mining technique, especially in the area of Web search. Various ranking schemes based on link analysis have been proposed, of which the PageRank metric has gained the most popularity with the success of Google. Over the last few years, there has been significant work in improving the relevance model of PageRank to address issues such as personalization and topic relevance. In addition, a variety of ideas have been proposed to address the computational aspects of PageRank, both in terms of efficient I/O computations and matrix computations involved in computing the PageRank score. The key challenge has been to perform computation on very large Web graphs. In this paper, we propose a method to incrementally compute PageRank for a large graph that is evolving. We note that although the Web graph evolves over time, its rate of change is rather slow. When compared to its size. We exploit the underlying principle of first order markov model on which PageRank is based, to incrementally compute PageRank for the evolving Web graph. Our experimental results show significant speed up in computational cost, the computation involves only the (small) portion of Web graph that has undergone change. Our approach is quite general, and can be used to incrementally compute (on evolving graphs) any metric that satisfies the first order Markov property.

Abstract-This paper presents a generalized version of the linear threshold model for simulating multiple cascades on a network while allowing nodes to switch between them. The proposed model is shown to be a rapidly mixing Markov chain and the corresponding steady state distribution is used to estimate highly likely states of the cascades' spread in the network. Results on a variety of real world networks demonstrate the high quality of the estimated solution.

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