# Rankings in directed configuration models with heavy tailed in-degrees

@article{Cai2021RankingsID, title={Rankings in directed configuration models with heavy tailed in-degrees}, author={Xing Shi Cai and Pietro Caputo and Guillem Perarnau and Matteo Quattropani}, journal={ArXiv}, year={2021}, volume={abs/2104.08389} }

We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by the directed configuration model. Under the assumption of bounded (2 + η)-moments on the in-degrees and of bounded out-degrees, we obtain tight comparisons between the maximum value of the stationary distribution and the maximum in-degree. Under the further assumption that the…

## 5 Citations

### PageRank asymptotics on directed preferential attachment networks

- MathematicsThe Annals of Applied Probability
- 2022

We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit…

### PAGERANK ASYMPTOTICS ON DIRECTED PREFERENTIAL ATTACHMENT NETWORKS BY SAYAN BANERJEE

- Mathematics
- 2021

We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit…

### On the meeting of random walks on random DFA

- Mathematics, Computer Science
- 2022

It is shown that, with high probability with respect to the generation of the graph, the meeting time of the two walks is stochastically dominated by a geometric random variable of rate (1+ o (1)) n − 1 , uniformly over their starting locations.

### Speeding up random walk mixing by starting from a uniform vertex

- MathematicsArXiv
- 2022

. The theory of rapid mixing random walksplaysa fundamentalrole in thestudyof modern randomised algorithms. Usually, the mixing timeis measuredwith respectto the worst initial position. It is well…

### The diameter of the directed configuration model

- MathematicsArXiv
- 2020

We show that the diameter of the directed configuration model with $n$ vertices rescaled by $\log n$ converges in probability to a constant. Our assumptions are the convergence of the in- and…

## References

SHOWING 1-10 OF 56 REFERENCES

### Typical distances in the directed configuration model

- MathematicsThe Annals of Applied Probability
- 2018

We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the…

### PageRank asymptotics on directed preferential attachment networks

- MathematicsThe Annals of Applied Probability
- 2022

We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit…

### Directed Random Graphs with given Degree Distributions

- Mathematics, Computer Science
- 2012

An algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G that with high probability will be graphical, that is, from which a simple directed graph can be drawn is proposed.

### Generalized PageRank on directed configuration networks

- MathematicsRandom Struct. Algorithms
- 2017

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 a stochastic fixed-point equation.

### Stationary distribution and cover time of sparse directed configuration models

- Mathematics
- 2019

We consider sparse digraphs generated by the configuration model with given in-degree and out-degree sequences. We establish that with high probability the cover time is linear up to a…

### Random graphs with arbitrary degree distributions and their applications.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

### Minimum stationary values of sparse random directed graphs

- MathematicsArXiv
- 2020

The stationary distribution of the simple random walk on the directed configuration model with bounded degrees is considered and it is shown that the minimum positive stationary value is whp $n^{-(1+C+o(1)$ for some constant $C \ge 0$ determined by the degree distribution.

### Cutoff at the “entropic time” for sparse Markov chains

- Mathematics
- 2016

We study convergence to equilibrium for a class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix P the mass is essentially…

### Extremal Dependencies and Rank Correlations in Power Law Networks

- Computer Science, MathematicsComplex
- 2009

It is demonstrated that the PageRank ranking is not sensitive to moderate changes in the damping factor, and a new measure for rank correlations is suggested, which is especially sensitive to rank permutations for top-ranked nodes.

### Random walk on sparse random digraphs

- Mathematics
- 2015

A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter…