Generalized PageRank on Directed Configuration Networks

Ningyuan Chen; Nelli  Litvak; Mariana Olvera-Cravioto

doi:10.1002/rsa.20700

Generalized PageRank on Directed Configuration Networks

Ningyuan Chen, Nelli Litvak, Mariana Olvera-Cravioto

Stochastic Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

Note: formula is not displayed correctly.

This paper studies the distribution of a family of rankings, which includes Google’s PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable R* that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to astochastic fixed-point equation of the form

R=^DΣ_i=1^N C_iR_i+ Q ,

where (Q,N, {C_i}) is a real-valued vector with N ∈ {0, 1, 2, . . . }, P(|Q| > 0) > 0, and the {R_i} are i.i.d. copies of R, independent of (Q,N, {C_i}). Moreover, we provide precise asymptotics for the limit R*, which when the in-degree distribution in the directed configuration model has a power law imply a power law distribution for R* with the same exponent.

Original language	English
Pages (from-to)	237-274
Number of pages	38
Journal	Random Structures and Algorithms
Volume	51
Issue number	2
DOIs	https://doi.org/10.1002/rsa.20700
Publication status	Published - 1 Sept 2017

Keywords

PageRank
ranking algorithms
irected conﬁguration model
complex networks
stochastic ﬁxed-point equations
Weighted branching processes
power laws

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10.1002/rsa.20700

Cite this

@article{7832703070594dd696188859fc0b7ce4,

title = "Generalized PageRank on Directed Configuration Networks",

abstract = "Note: formula is not displayed correctly. This paper studies the distribution of a family of rankings, which includes Google{\textquoteright}s PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable R* that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to astochastic fixed-point equation of the form R=DΣi=1N CiRi+ Q ,where (Q,N, {Ci}) is a real-valued vector with N ∈ {0, 1, 2, . . . }, P(|Q| > 0) > 0, and the {Ri} are i.i.d. copies of R, independent of (Q,N, {Ci}). Moreover, we provide precise asymptotics for the limit R*, which when the in-degree distribution in the directed configuration model has a power law imply a power law distribution for R* with the same exponent.",

keywords = "PageRank, ranking algorithms, irected conﬁguration model, complex networks, stochastic ﬁxed-point equations, Weighted branching processes, power laws",

author = "Ningyuan Chen and Nelli Litvak and Mariana Olvera-Cravioto",

year = "2017",

month = sep,

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doi = "10.1002/rsa.20700",

language = "English",

volume = "51",

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journal = "Random Structures and Algorithms",

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T1 - Generalized PageRank on Directed Configuration Networks

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AU - Litvak, Nelli

AU - Olvera-Cravioto, Mariana

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N2 - Note: formula is not displayed correctly. This paper studies the distribution of a family of rankings, which includes Google’s PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable R* that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to astochastic fixed-point equation of the form R=DΣi=1N CiRi+ Q ,where (Q,N, {Ci}) is a real-valued vector with N ∈ {0, 1, 2, . . . }, P(|Q| > 0) > 0, and the {Ri} are i.i.d. copies of R, independent of (Q,N, {Ci}). Moreover, we provide precise asymptotics for the limit R*, which when the in-degree distribution in the directed configuration model has a power law imply a power law distribution for R* with the same exponent.

AB - Note: formula is not displayed correctly. This paper studies the distribution of a family of rankings, which includes Google’s PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable R* that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to astochastic fixed-point equation of the form R=DΣi=1N CiRi+ Q ,where (Q,N, {Ci}) is a real-valued vector with N ∈ {0, 1, 2, . . . }, P(|Q| > 0) > 0, and the {Ri} are i.i.d. copies of R, independent of (Q,N, {Ci}). Moreover, we provide precise asymptotics for the limit R*, which when the in-degree distribution in the directed configuration model has a power law imply a power law distribution for R* with the same exponent.

KW - PageRank

KW - ranking algorithms

KW - irected conﬁguration model

KW - complex networks

KW - stochastic ﬁxed-point equations

KW - Weighted branching processes

KW - power laws

U2 - 10.1002/rsa.20700

DO - 10.1002/rsa.20700

M3 - Article

SN - 1042-9832

VL - 51

SP - 237

EP - 274

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 2

ER -

Generalized PageRank on Directed Configuration Networks

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Keywords

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