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Direct generation of random graphs exactly realising a prescribed degree sequence

Darko Obradovic, Maximilien Danisch
2014 2014 6th International Conference on Computational Aspects of Social Networks  
The direct generation of a simple network with a prescribed degree sequence still seems to be an open issue, since the prominent configuration model usually does not realise the degree distribution exactly  ...  In comparison to the switching Markov Chain Monte Carlo algorithms, the direct generation of edges allows an easy modification of the linking behaviour in the random graph, introducing for example degree  ...  ACKNOWLEDGEMENTS This reasearch was funded by the German Ministry of Education and Research (BMBF) in the NEXUS project, grant 01IW11001.  ... 
doi:10.1109/cason.2014.6920418 dblp:conf/cason/ObradovicD14 fatcat:7rlprltgpvhx7ov7kvw2pw5ycm

Construction and Random Generation of Hypergraphs with Prescribed Degree and Dimension Sequences [article]

Naheed Anjum Arafat, Debabrota Basu, Laurent Decreusefond, Stephane Bressan
2020 arXiv   pre-print
We propose algorithms for construction and random generation of hypergraphs without loops and with prescribed degree and dimension sequences.  ...  We also prove that the random generation algorithm generates any hypergraph following the prescribed degree and dimension sequences with a non-zero probability.  ...  Related Works Graphs with a Prescribed Degree Sequence There are two main frameworks for the generation of random graphs with a prescribed degree sequence.  ... 
arXiv:2004.05429v1 fatcat:s6jwfyboxrcd3dl4luwniake2a

Convergence law for hyper-graphs with prescribed degree sequences [article]

Nans Lefebvre
2015 arXiv   pre-print
It defines a random hyper-multigraph specified by two distributions, one for the degrees of the vertices, and one for the sizes of the hyper-edges.  ...  We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding  ...  a graph realising the degree sequence [4] .  ... 
arXiv:1501.07429v3 fatcat:bekcrtkkbrfanjgxwdzqk5b2vy

A permutation method for network assembly

Shawn A. Means, Christian Bläsche, Carlo R. Laing, Luc Berthouze
2020 PLoS ONE  
We present a method for assembling directed networks given a prescribed bi-degree (in- and out-degree) sequence.  ...  Given a sequence of in- and out- degrees, the method can also produce simple graphs for sequences that satisfy conditions of graphicality.  ...  Our implementation of this method includes a preliminary test ensuring the provided sequences of in-and out-degrees may actually realise a graph.  ... 
doi:10.1371/journal.pone.0240888 pmid:33095802 fatcat:tihp3es2kjecfeanam4e7ursqi

Analytical Formulation of the Block-Constrained Configuration Model [article]

Giona Casiraghi
2018 arXiv   pre-print
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model.  ...  These models provide a new, flexible tool for the study of community structure and for network science in general, where modelling networks with heterogeneous degree distributions is of central importance  ...  generated by the degree sequence of the observed graph.  ... 
arXiv:1811.05337v1 fatcat:h2ctanpzevcvjiczug6zp6gi4i

The block-constrained configuration model

Giona Casiraghi
2019 Applied Network Science  
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model.  ...  Block-constrained configuration models build on the generalized hypergeometric ensemble of random graphs and extend the well-known configuration model by enforcing block-constraints on the edge-generating  ...  generated by the degree sequence of the observed graph.  ... 
doi:10.1007/s41109-019-0241-1 fatcat:hukmen5gqncn7ouff6zsntwulu

Generating stationary random graphs on Z with prescribed i.i.d. degrees [article]

Maria Deijfen, Ronald Meester
2015 arXiv   pre-print
Two algorithms are described for generating a stationary random graph, with vertex set Z, so that the degrees of the vertices are i.i.d. random variables with distribution F.  ...  It is also shown that any stationary algorithm for pairing stubs with random, independent directions gives infinite mean for the total length of the edges of a given vertex.  ...  A different model for generating random graph with prescribed degrees is studied by Chung and Lu (2002:1,2) .  ... 
arXiv:1509.06989v1 fatcat:mx7xdmvkrjgardezlf7pexpite

Entropies of tailored random graph ensembles: bipartite graphs, generalised degrees, and node neighbourhoods [article]

Ekaterina Roberts, Ton Coolen
2014 arXiv   pre-print
We calculate explicit formulae for the Shannon entropies of several families of tailored random graph ensembles for which no such formulae were as yet available, in leading orders in the system size.  ...  These include bipartite graph ensembles with imposed (and possibly distinct) degree distributions for the two node sets, graph ensembles constrained by specified node neighbourhood distributions, and graph  ...  Acknowledgements ESR gratefully acknowledges financial support from the Biotechnology and Biological Sciences Research Council of the United Kingdom.  ... 
arXiv:1404.5786v1 fatcat:6ak5dpt3x5d6pcjg4u2q2n2t4a

Super-star networks: Growing optimal scale-free networks via likelihood [article]

Michael Small, Yingying Li, Thomas Stemler, Kevin Judd
2014 arXiv   pre-print
Our algorithm generates optimally scale-free networks (the super-star networks) as well as randomly sampling the space of all scale-free networks with a given degree exponent γ.  ...  the asymptotic probability of a node having degree k is proportional to k^-γ.  ...  However, BA does not generate random representative realisations from the set of all scale-free graphs [3, 4] .  ... 
arXiv:1305.6429v3 fatcat:rlmwiwgdj5hythxqn22anwjqaq

Expand and Contract: Sampling graphs with given degrees and other combinatorial families [article]

James Y. Zhao
2013 arXiv   pre-print
The utility of the method is demonstrated via several examples, with particular emphasis on sampling labelled graphs with given degree sequence, a well-studied problem for which existing algorithms leave  ...  We take advantage of such a relationship to describe a sampling algorithm for the smaller family, via a Markov chain started at a random sample of the larger family.  ...  . , d n ) is a degree sequence (that is, a sequence of positive integers which prescribes the degree at each vertex of a labelled graph); n denotes the number of vertices, m = 1 2 i d i denotes the number  ... 
arXiv:1308.6627v1 fatcat:kmk7c3mj4vhujnfthrt37btyqa

Growing optimal scale-free networks via likelihood

Michael Small, Yingying Li, Thomas Stemler, Kevin Judd
2015 Physical Review E  
asymptotic probability of a node having degree k is proportional to k −γ .  ...  We use exact likelihood arguments and show that the optimal way to build a scale-free network is to attach most new links to nodes of low degree.  ...  Mathematica and MATLAB implementations of the algorithms described in this paper are available from the first author.  ... 
doi:10.1103/physreve.91.042801 pmid:25974541 fatcat:qvqckdpdjzc7ldrwhiusv2yeeq

Bifurcations of mutually coupled equations in random graphs [article]

Eduardo Garibaldi, Tiago Pereira
2014 arXiv   pre-print
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs.  ...  We explicitly determine the bifurcation scenario in terms of the graph structure.  ...  We will use a random graph model and terminology from references [5, 6] . This model is an extension of the Erdös-Rényi model for random graphs with a general degree distribution.  ... 
arXiv:1409.5726v1 fatcat:duvspuyuh5dbbmjydof7wwpo6e

Generalized Bose-Fermi Statistics and Structural Correlations in Weighted Networks

Diego Garlaschelli, Maria I. Loffredo
2009 Physical Review Letters  
We derive a class of generalized statistics, unifying the Bose and Fermi ones, that describe any system where the first-occupation energies or probabilities are different from subsequent ones, as in presence  ...  Our results show that the null behavior of weighted networks is different from what previously believed, and that a systematic redefinition of weighted properties is necessary.  ...  The values of w, obtained for yiyj = FIG. 2 . 2 Analytical results for random networks with given strenght sequence generated by the distribution ρ(y) ∝ y −γ with (from top to bottom) γ = 1, 2, 3, 4.  ... 
doi:10.1103/physrevlett.102.038701 pmid:19257403 fatcat:mgi7o7wqx5f75hsqls5f6jnate

Generating graphs randomly [article]

Catherine Greenhill
2022 arXiv   pre-print
We will focus mainly on the set of all simple graphs with a particular degree sequence, and describe several different algorithms for sampling graphs from this family uniformly, or almost uniformly.  ...  Hence there is a need for algorithms which can generate graphs uniformly (or approximately uniformly) at random from the given family.  ...  More generally, we might be interested in bipartite graphs, directed graphs or hypergraphs with a given degree sequence.  ... 
arXiv:2201.04888v1 fatcat:efndo6y2dfgb7kgj7bxfk4yiiu

Bounds on the diameter of Cayley graphs of the symmetric group [article]

John Bamberg, Nick Gill, Thomas Hayes, Harald Helfgott, Ákos Seress, Pablo Spiga
2012 arXiv   pre-print
In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial  ...  We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.  ...  r is realised by the lazy random walk.  ... 
arXiv:1205.1596v1 fatcat:ybsspxooqzgwhj4bmie4qmii34
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