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...law behavior of the PageRank and its relation to the different characteristics of the underlying graph. To this end we propose a stochastic model that is a considerable extension of our previous work =-=[18, 27]-=-. The PageRank is modeled as a solution of a distributional identity, and the tail behavior of such solution is obtained under various assumptions on involved parameters. The generality of our analyti...

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...ed according to the in-degree distribution, and {Rj} are i.i.d random 1 M. Olvera-Cravioto/Linear recursions on trees 2 variables having the same distribution as R. This approach, first introduced in =-=[26]-=-, can be thought of as approximating the web graph with a branching tree, a well known technique used in the analysis of random graphs (see, e.g., [24] and the references therein). The fixed point equ...

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... totally different T -PageRanks. The critical temperature experimentally seems to be about T = 0.033. It has the same order of magnitude as the T ∗(n) = 0.06148 estimate discussed in Section 5. As in =-=[38]-=-, we represented in a log-log scale the cumulative distribution function of the PageRank, i.e the proportion of pages for which the T -PageRank is larger than a given value, as a function of this valu...

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...r, possibly also the same, sites per unit of time. The labels li, i = 1,2,...,N, can then be seen as differentiating frequencies of jumps to these sites. As formulated by Volkovich, Litvak and Donato =-=[7]-=-, Page Rank PR is a method for evaluating ” popularity of nodes in information networks”. It is therefore a kind of centrality measure. The basic modeling given by Brin and Page [1] is by an equation ...

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...� R (0) > x � = o(P(N > x)), then for all k ≥ 1, where Ck = P(R (k) > x) ∼ CkP(N > x) as x → ∞, � �α c(1−p0) �k−1 d j=0 cjαbj , and b = dE(1/Dα ). The form of the coefficient Ck arises from the proof =-=[12]-=-. For large enough k, Ck can be approximated by C = lim k→∞ Ck = cα (1 − p0) α d α (1 − c α b) . It follows that b ≥ (1 − p0) α d 1−α , and hence, (4) C ≥ c α (1 − p0) α d α (1 − c α (1 − p0) α d 1−α ...

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... nodes, graph diameter, etc. (see [7] for a recent survey and also [6, 24] for comprehensive texts on the subject). The recent interest in the analysis of ranking algorithms such as Google’s PageRank =-=[28, 27, 10]-=- is nonetheless more complex, since in addition to the fact that these type of algorithms are computed on directed graphs (as opposed to undirected ones), each node is assigned a vector of attributes,...

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...durangan et al. [16] discovered the interesting fact that PageRank scores also exhibit power laws, with the same exponent as the in-degree. This property holds for a broad class of real-life networks =-=[19]-=-. In fact, the hypothesis that this always holds in power-law networks is plausible. However, analytical mathematical evidence supporting this hypothesis is surprisingly scarce. As one of the few exam...