A unifying framework for fast randomization of ecological networks with fixed (node) degrees

Graphical abstract

[1]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[2]  Ravi Kannan,et al.  Markov chains and polynomial time algorithms , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[3]  László Lovász,et al.  Random Walks on Graphs: A Survey , 1993 .

[4]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[5]  J. Bascompte,et al.  Ecological networks : beyond food webs Ecological networks – beyond food webs , 2008 .

[6]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[7]  Noah Fierer,et al.  Using network analysis to explore co-occurrence patterns in soil microbial communities , 2011, The ISME Journal.

[8]  Eric Vigoda,et al.  Sampling binary contingency tables with a greedy start , 2006, SODA '06.

[9]  Catherine S. Greenhill.  A Polynomial Bound on the Mixing Time of a Markov Chain for Sampling Regular Directed Graphs , 2011, Electron. J. Comb..

[10]  F. Jotzo,et al.  Double counting and the Paris Agreement rulebook , 2019, Science.

[11]  Prasad Tetali,et al.  Simple Markov-Chain Algorithms for Generating Bipartite Graphs and Tournaments (Extended Abstract) , 1999, SODA.

[12]  Dieter Jungnickel,et al.  Graphs, Networks, and Algorithms , 1980 .

[13]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[14]  N. Verhelst.  An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals , 2008 .

[15]  Michael Drew Lamar.  On uniform sampling simple directed graph realizations of degree sequences , 2009, ArXiv.

[16]  Zoltán Toroczkai,et al.  New Classes of Degree Sequences with Fast Mixing Swap Markov Chain Sampling , 2016, Combinatorics, Probability and Computing.

[17]  Eric Vigoda,et al.  A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries , 2004, JACM.

[18]  Mark Jerrum,et al.  Approximating the Permanent , 1989, SIAM J. Comput..

[19]  Annabell Berger,et al.  The Connection between the Number of Realizations for Degree Sequences and Majorization , 2012, ArXiv.

[20]  Martin E. Dyer,et al.  Sampling regular graphs and a peer-to-peer network , 2005, SODA '05.

[21]  Sinan Aral,et al.  Identifying Influential and Susceptible Members of Social Networks , 2012, Science.

[22]  Timothy J. Purcell.  Sorting and searching , 2005, SIGGRAPH Courses.

[23]  N. Gotelli,et al.  EcoSim: Null models software for ecology , 2015 .

[24]  Giovanni Strona,et al.  A fast and unbiased procedure to randomize ecological binary matrices with fixed row and column totals , 2014, Nature Communications.

[25]  Stefano Allesina,et al.  Parasites in food webs: the ultimate missing links , 2008, Ecology letters.

[26]  Roded Sharan,et al.  The large-scale organization of the bacterial network of ecological co-occurrence interactions , 2010, Nucleic acids research.

[27]  Stefanie Widder,et al.  Deciphering microbial interactions and detecting keystone species with co-occurrence networks , 2014, Front. Microbiol..

[28]  Matthias Müller-Hannemann,et al.  Uniform sampling of undirected and directed graphs with a fixed degree sequence , 2009, ArXiv.

[29]  A. Rao,et al.  A Markov chain Monte carol method for generating random (0, 1)-matrices with given marginals , 1996 .

[31]  Catherine S. Greenhill.  The switch Markov chain for sampling irregular graphs (Extended Abstract) , 2014, SODA.

[32]  István Miklós,et al.  Towards Random Uniform Sampling of Bipartite Graphs with given Degree Sequence , 2010, Electron. J. Comb..

[33]  H. Ryser.  Combinatorial Properties of Matrices of Zeros and Ones , 1957, Canadian Journal of Mathematics.

[34]  Annabell Berger,et al.  A note on the characterization of digraphic sequences , 2011, Discret. Math..

[35]  Prasad Tetali,et al.  Simple Markov-chain algorithms for generating bipartite graphs and tournaments , 1997, SODA '97.

[36]  Samuel Johnson,et al.  Factors Determining Nestedness in Complex Networks , 2013, PloS one.

[37]  R. B. Eggleton,et al.  Simple and multigraphic realizations of degree sequences , 1981 .

[38]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[39]  C. J. Carstens,et al.  A uniform random graph model for directed acyclic networks and its effect on motif-finding , 2014, J. Complex Networks.

[40]  P. Flajolet.  On approximate counting , 1982 .

[41]  Neo D. Martinez.  Artifacts or Attributes? Effects of Resolution on the Little Rock Lake Food Web , 1991 .

[42]  Si Tang,et al.  Stability criteria for complex ecosystems , 2011, Nature.

[43]  Elizabeth L. Wilmer,et al.  Markov Chains and Mixing Times , 2008 .

[44]  A. Manica,et al.  Reducing over-reporting of deterministic co-occurrence patterns in biotic communities , 2010 .

[45]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Martin Dyer,et al.  Corrigendum: Sampling regular graphs and a peer-to-peer network , 2012 .

[47]  Matthias Müller-Hannemann,et al.  Uniform Sampling of Digraphs with a Fixed Degree Sequence , 2010, WG.

[48]  M. Moran,et al.  Large-scale mapping of human protein–protein interactions by mass spectrometry , 2007, Molecular systems biology.

[49]  W. T. Tutte.  The Factors of Graphs , 1952, Canadian Journal of Mathematics.

[50]  L. Stone,et al.  Generating uniformly distributed random networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Miguel B. Araújo,et al.  Using species co-occurrence networks to assess the impacts of climate change , 2011 .

[52]  Oliver D. King.  Comment on "Subgraphs in random networks". , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Mark Jerrum,et al.  Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains , 1987, International Workshop on Graph-Theoretic Concepts in Computer Science.

[54]  János Podani,et al.  RANDOMIZATION OF PRESENCE–ABSENCE MATRICES: COMMENTS AND NEW ALGORITHMS , 2004 .

[55]  Mark Jerrum,et al.  Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains , 1987, WG.

[56]  Thilo Gross,et al.  A general consumer-resource population model , 2015, Science.

[57]  C. J. Carstens.  Proof of uniform sampling of binary matrices with fixed row sums and column sums for the fast Curveball algorithm. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Giovanni Strona,et al.  A new measure of ecological network structure based on node overlap and segregation , 2015 .

[59]  M. Jerrum.  Counting, Sampling and Integrating: Algorithms and Complexity , 2003 .