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Convergence law for random graphs with specified degree sequence

2005
*
ACM Transactions on Computational Logic
*

A

doi:10.1145/1094622.1094627
fatcat:ml2jtqhiyjechjdwq65ackkglu
*random**graph**with**specified*asymptotic*degree**sequence*D is a*random**graph*on n*with**degree**sequence*d 0 (n), . . . , d n−1 (n)*for*some n ∈ ω. If • James F. ... Our*convergence**law*also extends the*convergence**law**for*classical*random**graphs**with*edge probability c/n, c constant [Lynch 1992] or*with**specified*number of edges cn/2. ...##
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Convergence law for random graphs with specified degree sequence

*
18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
*

Our main result is a

doi:10.1109/lics.2003.1210070
dblp:conf/lics/Lynch03
fatcat:5ck4ie4llnfn3cezejepiyyyju
*convergence**law**for**random**graphs**with**degree**sequences*approximated by some*sequence*λ 0 , λ 1 , . . . . ... A*random**graph**with**degree**sequence*d 0 , . . . , d n−1 is a randomly selected member of the set of*graphs*on {1, . . . , n}*with*that*degree**sequence*, all choices being equally likely. ... A*random**graph**with**specified*asymptotic*degree**sequence*D is a*random**graph*on n*with**degree**sequence*d 0 (n), . . . , d n−1 (n)*for*some n ∈ ω. If • James F. ...##
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Convergence law for hyper-graphs with prescribed degree sequences
[article]

2015
*
arXiv
*
pre-print

It defines a

arXiv:1501.07429v3
fatcat:bekcrtkkbrfanjgxwdzqk5b2vy
*random*hyper-multigraph*specified*by two distributions, one*for*the*degrees*of the vertices, and one*for*the sizes of the hyper-edges. ...*Convergence**laws*of other models follow, and in particular*for*the classical Erdős-Rényi*graphs*and k-uniform hyper-*graphs*. ...*graphs*(including the*graphs**with**specified**degree**sequences*), the¨-*graph*can be a sparse*graph**with*nontrivial clustering coefficient. ...##
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Local weak convergence for PageRank
[article]

2018
*
arXiv
*
pre-print

We start from the definition of local weak

arXiv:1803.06146v1
fatcat:oi2gdguchrg75irhymly7gkwke
*convergence**for**sequences*of (*random*) undirected*graphs*, and extend this notion to directed*graphs*. ... One of the intriguing empirical properties of PageRank is the so-called 'power-*law*hypothesis': in a scale-free network the PageRank scores follow a power*law**with*the same exponent as the (in-)*degrees*... The work of RvdH is further supported by the Netherlands Organisation*for*Scientific Research (NWO) through VICI grant 639.033.806. ...##
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Fast Generation of Sparse Random Kernel Graphs

2015
*
PLoS ONE
*

As a practical example we show how to generate samples of power-

doi:10.1371/journal.pone.0135177
pmid:26356296
pmcid:PMC4565681
fatcat:qvinadyfxrahhjhrpanvusagqa
*law**degree*distribution*graphs**with*tunable assortativity. ... We*specify*a class of inhomogeneous*random**graph*models, called*random*kernel*graphs*, that produces sparse*graphs**with*tunable*graph*properties, and we develop an efficient generation algorithm to sample ... Acknowledgments We would like to thank Terry Haut, Joel Miller, and Pieter Swart*for*helpful comments and suggestions. Author Contributions Conceived and designed the experiments: AH NL. ...##
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Counting triangles in power-law uniform random graphs
[article]

2018
*
arXiv
*
pre-print

We count the asymptotic number of triangles in uniform

arXiv:1812.04289v1
fatcat:t6ew6pzlwfclhdlfiecitxg3t4
*random**graphs*where the*degree*distribution follows a power*law**with**degree*exponent τ∈(2,3). ... Interestingly, uniform*random**graphs*contain more triangles than erased configuration models*with*the same*degree**sequence*. ... Other methods*for*analyzing uniform*random**graphs*rely on asymptotic enumeration of*graphs**with**specified**degree**sequences*. ...##
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Counting Triangles in Power-Law Uniform Random Graphs

2020
*
Electronic Journal of Combinatorics
*

We count the asymptotic number of triangles in uniform

doi:10.37236/9239
fatcat:h72m65wjjvftzf5tcmu6xses7a
*random**graphs*where the*degree*distribution follows a power*law**with**degree*exponent $\tau\in(2,3)$. ... Interestingly, uniform*random**graphs*contain more triangles than erased configuration models*with*the same*degree**sequence*. ... We thank an anonymous referee*for*pointing out how the integrals in (4.32) and (5.32) could be computed. ...##
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Tracking a Markov-Modulated Stationary Degree Distribution of a Dynamic Random Graph

2014
*
IEEE Transactions on Information Theory
*

This paper considers a Markov-modulated duplication-deletion

doi:10.1109/tit.2014.2346183
fatcat:htwyf4ffyreqphlkhvmh52iqqm
*random**graph*where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according ... First, motivated by social network applications, the asymptotic behavior of the*degree*distribution is analyzed. ... Fig. 1 . 1 The*degree*distribution of the duplication-deletion*random**graph*satisfies a power*law*. The parameters are*specified*in Example 1 of Sec.VI. ...##
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Universality for distances in power-law random graphs

2008
*
Journal of Mathematical Physics
*

Since many real network have been empirically shown to have power-

doi:10.1063/1.2982927
fatcat:eipdks45qrgtbf4ltyxxokssre
*law**degree**sequences*, these*random**graphs*can be seen as more realistic models*for*real complex networks. ... We focus on inhomogeneous*random**graphs*, the configuration model and affine preferential attachment models, and pay special attention to setting where these*random**graphs*have a power-*law**degree**sequence*... Indeed, as proved in [17] , the generalized*random**graph*, conditioned on its*degree**sequence*, is a uniform simple*random**graph**with*that*degree**sequence*. ...##
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Moment-Based Spectral Analysis of Random Graphs with Given Expected Degrees
[article]

2017
*
arXiv
*
pre-print

Under some technical conditions on the expected

arXiv:1512.03489v3
fatcat:az3l4ubfgrgyfeynck3nnck6qe
*degree**sequence*, we show that*with*probability one, F_n(·)*converges*weakly to a deterministic distribution F(·). ... In this paper, we analyze the limiting spectral distribution of the adjacency matrix of a*random**graph*ensemble, proposed by Chung and Lu, in which a given expected*degree**sequence*w_n^^T = (w^(n)_1,.. ... Then, consider a Chung-Lu*random**graph**with*the expected*degree**sequence**specified*as w (n) i = ∆ n e −αxi , i ∈ [n] . ...##
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Sampling random graphs with specified degree sequences
[article]

2022
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arXiv
*
pre-print

The configuration model is a standard tool

arXiv:2105.12120v2
fatcat:uwv7pewizfgupbrzglhbvee2x4
*for*uniformly generating*random**graphs**with*a*specified**degree**sequence*, and is often used as a null model to evaluate how much of an observed network's structure ... We develop an algorithm, based on the assortativity of the sampled*graphs*,*for*estimating the gap between effectively independent MCMC states, and a computationally efficient gap-estimation heuristic derived ... The authors thank Joel Nishimura*for*providing the Python code*for*checking if the loopy*graph*space is connected or not. ...##
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Random-walk models of network formation and sequential Monte Carlo methods for graphs

2018
*
Journal of The Royal Statistical Society Series B-statistical Methodology
*

Theoretical properties, including the limiting

doi:10.1111/rssb.12289
fatcat:uxbe6jaoqjaztdpg4utgoyi7aq
*degree**sequence*, are studied analytically. If the entire history of the*graph*is observed, parameters can be estimated by maximum likelihood. ... We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a*random*walk on the network*graph*. ... A*random**sequence*G 1:T can then be*specified*as a pair (Π, G T ),*for*a*random*permutation Π of the edges in G T ,*with*G t = Π t (G T ). ...##
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Resolvent of large random graphs

2010
*
Random structures & algorithms (Print)
*

We illustrate our results on the uniform regular

doi:10.1002/rsa.20313
fatcat:nbwhktvg75ekpnbxsvhlp7sja4
*graphs*, Erdös-Rényi*graphs*and*graphs**with*a given*degree**sequence*. ... We analyze the*convergence*of the spectrum of large*random**graphs*to the spectrum of a limit infinite*graph*. ... Acknowledgment The authors thank Noureddine El Karoui*for*fruitful discussions and his interest in this work. ...##
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Resolvent of Large Random Graphs
[article]

2009
*
arXiv
*
pre-print

We analyze the

arXiv:0801.0155v3
fatcat:oekfsjb6qbbl7oc3iqtu7zc3ra
*convergence*of the spectrum of large*random**graphs*to the spectrum of a limit infinite*graph*. ... We apply these results to*graphs**converging*locally to trees and derive a new formula*for*the Stieljes transform of the spectral measure of such*graphs*. ... Acknowledgment The authors thank Noureddine El Karoui*for*fruitful discussions and his interest in this work. ...##
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Graph Signal Processing: Filter Design and Spectral Statistics
[article]

2018
*
arXiv
*
pre-print

An application considered in this paper,

arXiv:1802.10145v1
fatcat:wjkyr7mdgbcjfc45hvu3566uu4
*convergence*acceleration filters*for*distributed average consensus may be viewed as lowpass*graph*filters periodically applied to the states. ...*With*respect to the*graph*shift operator, polynomial functions of the shift matrix perform filtering. ... the*convergence*rate*for*large scale constant (*with*respect to time iterations)*random*networks. ...
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