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Direct generation of random graphs exactly realising a prescribed degree sequence

2014
*
2014 6th International Conference on Computational Aspects of Social Networks
*

The

doi:10.1109/cason.2014.6920418
dblp:conf/cason/ObradovicD14
fatcat:7rlprltgpvhx7ov7kvw2pw5ycm
*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. ...##
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Construction and Random Generation of Hypergraphs with Prescribed Degree and Dimension Sequences
[article]

2020
*
arXiv
*
pre-print

We propose algorithms for construction and

arXiv:2004.05429v1
fatcat:s6jwfyboxrcd3dl4luwniake2a
*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*. ...##
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Convergence law for hyper-graphs with prescribed degree sequences
[article]

2015
*
arXiv
*
pre-print

It defines

arXiv:1501.07429v3
fatcat:bekcrtkkbrfanjgxwdzqk5b2vy
*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] . ...##
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A permutation method for network assembly

2020
*
PLoS ONE
*

We present

doi:10.1371/journal.pone.0240888
pmid:33095802
fatcat:tihp3es2kjecfeanam4e7ursqi
*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*. ...##
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Analytical Formulation of the Block-Constrained Configuration Model
[article]

2018
*
arXiv
*
pre-print

We provide

arXiv:1811.05337v1
fatcat:h2ctanpzevcvjiczug6zp6gi4i
*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*. ...##
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The block-constrained configuration model

2019
*
Applied Network Science
*

We provide

doi:10.1007/s41109-019-0241-1
fatcat:hukmen5gqncn7ouff6zsntwulu
*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*. ...##
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Generating stationary random graphs on Z with prescribed i.i.d. degrees
[article]

2015
*
arXiv
*
pre-print

Two algorithms are described for

arXiv:1509.06989v1
fatcat:mx7xdmvkrjgardezlf7pexpite
*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) . ...##
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Entropies of tailored random graph ensembles: bipartite graphs, generalised degrees, and node neighbourhoods
[article]

2014
*
arXiv
*
pre-print

We calculate explicit formulae for the Shannon entropies

arXiv:1404.5786v1
fatcat:6ak5dpt3x5d6pcjg4u2q2n2t4a
*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. ...##
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Super-star networks: Growing optimal scale-free networks via likelihood
[article]

2014
*
arXiv
*
pre-print

Our algorithm

arXiv:1305.6429v3
fatcat:rlmwiwgdj5hythxqn22anwjqaq
*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] . ...##
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Expand and Contract: Sampling graphs with given degrees and other combinatorial families
[article]

2013
*
arXiv
*
pre-print

The utility

arXiv:1308.6627v1
fatcat:kmk7c3mj4vhujnfthrt37btyqa
*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 ...##
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Growing optimal scale-free networks via likelihood

2015
*
Physical Review E
*

asymptotic probability

doi:10.1103/physreve.91.042801
pmid:25974541
fatcat:qvqckdpdjzc7ldrwhiusv2yeeq
*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. ...##
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Bifurcations of mutually coupled equations in random graphs
[article]

2014
*
arXiv
*
pre-print

We study the behavior

arXiv:1409.5726v1
fatcat:duvspuyuh5dbbmjydof7wwpo6e
*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. ...##
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Generalized Bose-Fermi Statistics and Structural Correlations in Weighted Networks

2009
*
Physical Review Letters
*

We derive

doi:10.1103/physrevlett.102.038701
pmid:19257403
fatcat:mgi7o7wqx5f75hsqls5f6jnate
*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. ...##
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Generating graphs randomly
[article]

2022
*
arXiv
*
pre-print

We will focus mainly on the set

arXiv:2201.04888v1
fatcat:efndo6y2dfgb7kgj7bxfk4yiiu
*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*. ...##
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Bounds on the diameter of Cayley graphs of the symmetric group
[article]

2012
*
arXiv
*
pre-print

In this paper we are concerned with the conjecture that, for any set

arXiv:1205.1596v1
fatcat:ybsspxooqzgwhj4bmie4qmii34
*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. ...
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