Black hole metric: Overcoming the pagerank normalization problem

Buzzanca, Marco; Carchiolo, Vincenza; Longheu, Alessandro; Malgeri, Michele; Mangioni, Giuseppe

doi:10.1016/j.ins.2018.01.033

Cited by 17 publications

(4 citation statements)

References 38 publications

(39 reference statements)

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“…Much effort for accelerating the PageRank algorithm has been carried out from different view, such as Monte Carlo method [16], random walk [17], power method or general linear system [18,19], graph theory [20, 21,22], Schrödinger equation [23], and quantum networks [24,25]. More recent related advances on this topic can be found in [26,27,28,29,30,31,32,33,34,35,36].…”

Section: Related Workmentioning

confidence: 99%

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Two-hop walks indicate PageRank order

Tang

2019

Pattern Recognition

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This paper shows that pairwise PageRank orders emerge from two-hop walks.The main tool used here refers to a specially designed sign-mirror function and a parameter curve, whose low-order derivative information implies pairwise PageRank orders with high probability. We study the pairwise correct rate by placing the Google matrix G in a probabilistic framework, where G may be equipped with different random ensembles for model-generated or realworld networks with sparse, small-world, scale-free features, the proof of which is mixed by mathematical and numerical evidence. We believe that the underlying spectral distribution of aforementioned networks is responsible for the high pairwise correct rate. Moreover, the perspective of this paper naturally leads to an O(1) algorithm for any single pairwise PageRank comparison if assuming both A = G − I n , where I n denotes the identity matrix of order n, and A 2 are ready on hand (e.g., constructed offline in an incremental manner), based on which it is easy to extract the top k list in O(kn), thus making it possible for PageRank algorithm to deal with super large-scale datasets in real time.

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Section: Related Workmentioning

confidence: 99%

“…Schrödinger equation [23], and quantum networks [24,25]. More recent related advances on this topic can be found in [26,27,28,29,30,31,32,33,34,35,36].…”

Section: Related Workmentioning

confidence: 99%

Two-hop walks indicate PageRank order

Tang

2019

Pattern Recognition

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“…36,37 PageRank is also used as a reference model to compare rankings that use new techniques. 18 PageRank has also recently been used to analyze opinion formation, 28 for networks that change with time while preserving their nodes, 42 to analyze risk in financial networks, 62 to include the concept of trust on weighted social networks, 15 to study the vulnerability of gas and electricity networks, 55 to rank citation networks, 44 and to rank products following multiple criteria in dynamic markets. 54 There are also new numerical methods for the PageRank algorithm (see Ref.…”

Section: Introductionmentioning

confidence: 99%

Parametric controllability of the personalized PageRank: Classic model vs biplex approach

Flores

Garcı́a

Pedroche

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Measures of centrality in networks defined by means of matrix algebra, like PageRank-type centralities, have been used for over 70 years. Recently, new extensions of PageRank have been formulated and may include a personalization (or teleportation) vector. It is accepted that one of the key issues for any centrality measure formulation is to what extent someone can control its variability. In this paper, we compare the limits of variability of two centrality measures for complex networks that we call classic PageRank (PR) and biplex approach PageRank (BPR). Both centrality measures depend on the so-called damping parameter α that controls the quantity of teleportation. Our first result is that the intersection of the intervals of variation of both centrality measures is always a nonempty set. Our second result is that when α is lower that 0.48 (and, therefore, the ranking is highly affected by teleportation effects) then the upper limits of PR are more controllable than the upper limits of BPR; on the contrary, when α is greater than 0.5 (and we recall that the usual PageRank algorithm uses the value 0.85), then the upper limits of PR are less controllable than the upper limits of BPR, provided certain mild assumptions on the local structure of the graph. Regarding the lower limits of variability, we give a result for small values of α. We illustrate the results with some analytical networks and also with a real Facebook network.

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“…The method of calculating the PR is essential for our experiment. There are many different methods for calculating the PR [4][5][6][7], and we try to find the ideal one for our method of finding differences between expected and observed probability of accesses to web pages. We are also looking for the ideal value of the damping factor, which will be discussed later.…”

Section: Introductionmentioning

confidence: 99%

Selection of Suitable PageRank Calculation for Analysis of Differences Between Expected and Observed Probability of Accesses to Web Pages

Kapusta

Munk

Švec

2018

Lecture Notes in Computer Science

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We describe various approaches how to calculate the value of Pag-eRank in this paper. There are few methods how to calculate the PageRank, from the basic historical one to more enhanced versions. Most of them are using the original value of the damping factor. We describe the experiment we realised using our method for analysing differences between expected and observed probability of accesses to web pages of the selected portal. We used five slightly different methods for PageRank estimation using both the original value of damping factor and the value calculated from data in the web server log file. We assumed and confirmed that the estimation/calculation of the damping factor would have a significant impact on the estimation of the PageRank. We also wrongly assumed that the estimation/calculation of the damping factor would have a significant impact on the number of suspicious pages. We also compared the computational complexity of used PageRank methods, and the most effective method seems to be a method with the estimated value of the damping factor.

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Black hole metric: Overcoming the pagerank normalization problem

Cited by 17 publications

References 38 publications

Two-hop walks indicate PageRank order

Two-hop walks indicate PageRank order

Parametric controllability of the personalized PageRank: Classic model vs biplex approach

Selection of Suitable PageRank Calculation for Analysis of Differences Between Expected and Observed Probability of Accesses to Web Pages

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