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

10/28/2021
βˆ™
by   Daniel Allendorf, et al.
βˆ™
0
βˆ™

We consider the following common network analysis problem: given a degree sequence 𝐝 = (d_1, …, d_n) βˆˆβ„•^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 generating graphs for power-law bounded degree sequences with Ξ³βͺ† 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 open-source implementation of Inc-Powerlaw is the first practical generator with rigorous uniformity guarantees for the aforementioned degree sequences. In an empirical investigation, we find that for small average-degrees Inc-Powerlaw is very efficient and generates graphs with one million nodes in less than a second. For larger average-degrees, parallelism can partially mitigate the increased running-time.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 21

βˆ™ 05/09/2019

Fast uniform generation of random graphs with given degree sequences

In this paper we provide an algorithm that generates a graph with given ...
βˆ™ 09/08/2020

Connectedness matters: Construction and exact random sampling of connected graphs

We describe a new method for the random sampling of connected networks w...
βˆ™ 11/04/2021

Parallel Global Edge Switching for the Uniform Sampling of Simple Graphs with Prescribed Degrees

The uniform sampling of simple graphs matching a prescribed degree seque...
βˆ™ 06/01/2021

Construction of Simplicial Complexes with Prescribed Degree-Size Sequences

We study the realizability of simplicial complexes with a given pair of ...
βˆ™ 05/16/2019

Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs

Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs...
βˆ™ 04/16/2021

Rankings in directed configuration models with heavy tailed in-degrees

We consider the extremal values of the stationary distribution of sparse...
βˆ™ 05/09/2019

Linear Work Generation of R-MAT Graphs

R-MAT is a simple, widely used recursive model for generating `complex n...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.