• Corpus ID: 239016992

Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals

  title={Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals},
  author={Georgios Amanatidis and Pieter Kleer},
The approximate uniform sampling of graphs with a given degree sequence is a well-known, extensively studied problem in theoretical computer science and has significant applications, e.g., in the analysis of social networks. In this work we study an extension of the problem, where degree intervals are specified rather than a single degree sequence. We are interested in sampling and counting graphs whose degree sequences satisfy the degree interval constraints. A natural scenario where this… 

Figures from this paper


Asymptotic enumeration of graphs by degree sequence, and the degree sequence of a random graph
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. This confirms a conjecture made in 1997. As
Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs
A straightforward application of this latter result shows that when a random bipartite or directed graph is generated under the Erdős—Rényi G(n, p) model with mild assumptions on n and p then the degree sequence of the generated graph has, with high probability, a rapidly mixing swap Markov chain on its realizations.
The switch Markov chain for sampling irregular graphs and digraphs
It is proved that the switch chain for undirected graphs is rapidly mixing for any degree sequence with minimum degree at least 1 and with maximum degree $d_{\max}$ which satisfies $3\leq d_{\ max}\leq \frac{1}{3}\, \sqrt{M}$, where $M$ is the sum of the degrees.
Uniform generation of random graphs with power-law degree sequences
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.
A Sequential Algorithm for Generating Random Graphs
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.
Sampling hypergraphs with given degrees
This work describes and analyzes a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence, and gives some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a constant.
Fast Uniform Generation of Regular Graphs
The algorithm is based on simulation of a rapidly convergent stochastic process, and runs in polynomial time for a wide class of degree sequences, including all regular sequences and all n -vertex sequences with no degree exceeding √ n /2.
Asymptotic Enumeration by Degree Sequence of Graphs of High Degree
This work considers the estimation of the number of labelled simple graphs with degree sequence d 1, d 2, . . . , d n by using an n-dimensional Cauchy integral and gives as a corollary the asymptotic joint distribution function of the degrees of a random graph.
Speeding up Switch Markov Chains for Sampling Bipartite Graphs with Given Degree Sequence
This work presents the first results regarding the mixing time of the Curveball algorithm, and gives a theoretical comparison between the switch and Curveball algorithms in terms of their underlying Markov chains.
A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees
An extension of a combinatorial characterization due to Erdős and Gallai is used to develop a sequential algorithm for generating a random labeled graph with a given degree sequence, which allows for surprisingly efficient sequential importance sampling.