Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Seven criteria for integer sequences bring graphic
Journal of Graph Theory
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
Efficient generation of graphical partitions
Discrete Applied Mathematics
Assessing data mining results via swap randomization
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Towards identity anonymization on graphs
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Proceedings of the 14th International Conference on Extending Database Technology
Hamilton Cycles in Random Graphs with a Fixed Degree Sequence
SIAM Journal on Discrete Mathematics
Efficient and simple generation of random simple connected graphs with prescribed degree sequence
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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The graphs that arise from concrete applications seem to correspond to models with prescribed degree sequences. We present two algorithms for the uniform random generation of graphic sequences. We prove their correctness. We empirically evaluate their performance. To our knowledge these algorithms are the first non trivial algorithms proposed for this task. The algorithms that we propose are Markov chain Monte Carlo algorithms. Our contribution is the original design of the Markov chain and the empirical evaluation of mixing time.