| Abstract: | 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  that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to a stochastic fixed‐point equation of the form ![]() where  is a real‐valued vector with  , and the  are i.i.d. copies of  , independent of  . Moreover, we provide precise asymptotics for the limit  , which when the in‐degree distribution in the directed configuration model has a power law imply a power law distribution for  with the same exponent. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 237–274, 2017 |
that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to a stochastic fixed‐point equation of the form 
is a real‐valued vector with 
, and the 
are i.i.d. copies of 
, independent of 
. Moreover, we provide precise asymptotics for the limit 
, which when the in‐degree distribution in the directed configuration model has a power law imply a power law distribution for 
with the same exponent. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 237–274, 2017