Engineering Uniform Sampling of Graphs with a Prescribed Powerlaw Degree Sequence
Abstract
We consider the following common network analysis problem: given a degree sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ 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 EdgeSwitching or Curveball, even if no practical useful rigorous bounds are known on their mixing times. In contrast, Arman et al. sketch IncPowerlaw, a novel and much more involved algorithm capable of generating graphs for powerlaw bounded degree sequences with $\gamma \gtrapprox 2.88$ in expected linear time. For the first time, we give a complete description of the algorithm and add novel switchings. To the best of our knowledge, our opensource implementation of IncPowerlaw is the first practical generator with rigorous uniformity guarantees for the aforementioned degree sequences. In an empirical investigation, we find that for small averagedegrees IncPowerlaw is very efficient and generates graphs with one million nodes in less than a second. For larger averagedegrees, parallelism can partially mitigate the increased runningtime.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.15015
 Bibcode:
 2021arXiv211015015A
 Keywords:

 Computer Science  Data Structures and Algorithms;
 G.2.2
 EPrint:
 Scheduled for presentation at ALENEX 2022