TY - BOOK

T1 - Ranking algorithms on directed configuration networks

AU - Chen, Ningyuan

AU - Litvak, Nelli

AU - Olvera-Cravioto, Mariana

PY - 2015/6/16

Y1 - 2015/6/16

N2 - 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 endogenous solution to a stochastic fixed point equation of the form $R \stackrel {D}{=} \sum^N _{i=1} C_iR_i + Q,$ where $(Q,N, \{C_i\})$ is a real-valued vector with $N \in \{0, 1, 2, ... \}$, $P(|Q| > 0) > 0$, 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.

AB - 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 endogenous solution to a stochastic fixed point equation of the form $R \stackrel {D}{=} \sum^N _{i=1} C_iR_i + Q,$ where $(Q,N, \{C_i\})$ is a real-valued vector with $N \in \{0, 1, 2, ... \}$, $P(|Q| > 0) > 0$, 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.

KW - PageRank

KW - Stochastic fixed-point equations

KW - Ranking algorithms

KW - Weighted branching processes

KW - Directed configuration model

KW - Complex networks

KW - IR-96268

KW - METIS-312642

KW - MSC-68P20

KW - MSC-60J80

KW - MSC-05C80

KW - EWI-26087

KW - Power laws

M3 - Report

T3 - Memorandum of the Department of Applied Mathematics

BT - Ranking algorithms on directed configuration networks

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -