How hard is it to marry at random? (On the approximation of the permanent)
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Fast uniform generation of regular graphs
Theoretical Computer Science
The Stanford GraphBase: a platform for combinatorial computing
The Stanford GraphBase: a platform for combinatorial computing
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
Random Structures & Algorithms
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The degree sequence of a scale-free random graph process
Random Structures & Algorithms
The "DGX" distribution for mining massive, skewed data
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Generating Random Regular Graphs Quickly
Combinatorics, Probability and Computing
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Systematic topology analysis and generation using degree correlations
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
Generating Random Regular Graphs
Combinatorica
Orbis: rescaling degree correlations to generate annotated internet topologies
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
Statistical properties of community structure in large social and information networks
Proceedings of the 17th international conference on World Wide Web
Power-Law Distributions in Empirical Data
SIAM Review
Kronecker Graphs: An Approach to Modeling Networks
The Journal of Machine Learning Research
A geometric preferential attachment model of networks II
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
A Sequential Algorithm for Generating Random Graphs
Algorithmica
An In-depth Study of Stochastic Kronecker Graphs
ICDM '11 Proceedings of the 2011 IEEE 11th International Conference on Data Mining
Are we there yet? when to stop a markov chain while generating random graphs
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
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One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real-life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, that is, the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative. We suggest understanding the relationship between network structure and the joint degree distribution of graphs is an interesting avenue of further research. An important tool for such studies are algorithms that can generate random instances of graphs with the same joint degree distribution. This is the main topic of this article, and we study the problem from both a theoretical and practical perspective. We provide an algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via endpoint switches. We empirically evaluate the mixing time of this Markov chain by using experiments based on the autocorrelation of each edge. These experiments show that our Markov chain mixes quickly on these real graphs, allowing for utilization of our techniques in practice.