# Engineering Uniform Sampling of Graphs with a Prescribed Power-law Degree Sequence

@article{Allendorf2022EngineeringUS, title={Engineering Uniform Sampling of Graphs with a Prescribed Power-law Degree Sequence}, author={Daniel J Allendorf and Ulrich Meyer and Manuel Penschuck and Hung Tran and Nicholas C. Wormald}, journal={ArXiv}, year={2022}, volume={abs/2110.15015} }

We consider the following common network analysis problem: given a degree sequence d = (d1, . . . , dn) ∈ N return a uniform sample from the ensemble of all simple graphs with matching degrees. In practice, the problem is typically solved using Markov Chain Monte Carlo approaches, such as Edge-Switching or Curveball, even if no practical useful rigorous bounds are known on their mixing times. In contrast, Arman et al. sketch Inc-Powerlaw, a novel and much more involved algorithm capable of…

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SHOWING 1-10 OF 51 REFERENCES

Uniform generation of random graphs with power-law degree sequences

- Mathematics, Computer ScienceSODA
- 2018

This work gives a linear-time algorithm that approximately uniformly generates a random simple graph with a power-law degree sequence whose exponent is at least 2.8811 and shows that with an appropriate rejection scheme, this algorithm can be tuned into an exact uniform sampler.

Fast Uniform Generation of Random Graphs with Given Degree Sequences

- Mathematics, Computer Science2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

An algorithm that generates a graph with given degree sequence uniformly at random in expected time O(m) is provided, and this algorithm significantly improves the previously most efficient uniform sampler.

On the uniform generation of random graphs with prescribed degree sequences

- Mathematics, Physics
- 2003

A new method based on the ``go with the winners'' Monte Carlo method is presented, which can be used to evaluate the reliability of the other two methods and demonstrate that the deviations of the switching and matching algorithms under realistic conditions are small.

Sampling Graphs with a Prescribed Joint Degree Distribution Using Markov Chains

- Mathematics, Computer ScienceALENEX
- 2011

It is suggested that the joint degree distribution of graphs is an interesting avenue of study for further research into network structure and a simple greedy algorithm for constructing simple graphs from a given joint degree distributions, and a Monte Carlo Markov Chain method for sampling them.

A Sequential Algorithm for Generating Random Graphs

- Mathematics, Computer ScienceAlgorithmica
- 2009

A nearly-linear time algorithm for counting and randomly generating simple graphs with a given degree sequence in a certain range and it is shown that for d=O(n1/2−τ), the algorithm can generate an asymptotically uniform d-regular graph.

The Markov Chain Simulation Method for Generating Connected Power Law Random Graphs

- Mathematics, Computer ScienceALENEX
- 2003

This paper introduces a novel heuristic to speed up the simulation of the Markov chain, and uses metrics reminiscent of quality of service and congestion to evaluate the output graphs.

Different flavors of randomness: comparing random graph models with fixed degree sequences

- Mathematics, Computer ScienceSocial Network Analysis and Mining
- 2015

Whether one of the following three approximative models can replace the fixed degree sequence model (FDSM): the configuration model, its simplified version (eCFG), and the mathematical approximation the authors term simple independence model are discussed.

Efficient and Simple Generation of Random Simple Connected Graphs with Prescribed Degree Sequence

- Computer ScienceCOCOON
- 2005

This work addresses the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence and obtains an On log n algorithm, which, in spite of being very simple, improves the best known complexity.

The switch Markov chain for sampling irregular graphs (Extended Abstract)

- Computer Science, MathematicsSODA
- 2015

It is proved that the switch chain is rapidly mixing for any degree sequence with minimum degree at least 1 and with maximum degree d_{\max} which satisfies 3-2-1-4, where d is the sum of the degrees and 1-4 is the number of vertices.

Simple Markov-chain algorithms for generating bipartite graphs and tournaments

- Mathematics, Computer ScienceSODA '97
- 1997

A simple Markov chain has one state for every graph (or bipartite graph) with the given degree sequence; in particular, there are no auxiliary states as in the chain used by Jerrum and Sinclair.