The choice of the PageRank damping factor is not evident. The Google's choice for the value c = 0.85 was a compromise between the true reflection of the Web structure and numerical efficiency. However, the Markov random walk on the original Web Graph does not reflect the importance of the pages because it absorbs in dead ends. Thus, the damping factor is needed not only for speeding up the computations but also for establishing a fair ranking of pages. In this paper, we propose new criteria for choosing the damping factor, based on the ergodic structure of the Web Graph and probability flows. Specifically, we require that the core component receives a fair share of the PageRank mass. Using singular perturbation approach we conclude that the value c = 0.85 is too high and suggest that the damping factor should be chosen around 1/2. As a by-product, we describe the ergodic structure of the OUT component of the Web Graph in detail. Our analytical results are confirmed by experiments on two large samples of the Web Graph.

We study the PageRank mass of principal components in a bow-tie Web Graph, as a function of the damping factor c. Using a singular perturbation approach, we show that the PageRank share of IN and SCC components remains high even for very large values of the damping factor, in spite of the fact that it drops to zero when c → 1. However, a detailed study of the OUT component reveals the presence "dead-ends" (small groups of pages linking only to each other) that receive an unfairly high ranking when c is close to one. We argue that this problem can be mitigated by choosing c as small as 1/2.

Reputation systems are indispensable for the operation of Internet mediated services, electronic markets, document ranking systems, P2P networks and Ad Hoc networks. Here we survey available distributed approaches to the graph based reputation measures. Graph based reputation measures can be viewed as random walks on directed weighted graphs whose edges represent interactions among peers. We classify the distributed approaches to graph based reputation measures into three categories. The first category is based on asynchronous methods. The second category is based on the aggregation/decomposition methods. And the third category is based on the personalization methods which use local information.

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This tutorial teaches users how to create a web map based on tabular data.