scholarly journals Random graphs with a given degree sequence

2011 ◽  
Vol 21 (4) ◽  
pp. 1400-1435 ◽  
Author(s):  
Sourav Chatterjee ◽  
Persi Diaconis ◽  
Allan Sly
Keyword(s):  
Random Graphs ◽  
Degree Sequence

scholarly journals A Note on the Warmth of Random Graphs with Given Expected Degrees

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Statistical Mechanics ◽  
Chromatic Number ◽  
Random Graph ◽  
Lower Bounds ◽  
Random Graphs ◽  
Upper Bound ◽  
Degree Sequence ◽  
Graph Model ◽  
Upper And Lower Bounds ◽  
Random Graph Model

We consider the random graph modelG(w)for a given expected degree sequencew=(w1,w2,…,wn). Warmth, introduced by Brightwell and Winkler in the context of combinatorial statistical mechanics, is a graph parameter related to lower bounds of chromatic number. We present new upper and lower bounds on warmth ofG(w). In particular, the minimum expected degree turns out to be an upper bound of warmth when it tends to infinity and the maximum expected degreem=O(nα)with0<α<1/2.

Directed weighted random graphs with an increasing bi-degree sequence

2016 ◽  
Vol 119 ◽  
pp. 235-240 ◽  
Author(s):  
Zhang Yong ◽  
Siyu Chen ◽  
Hong Qin ◽  
Ting Yan
Keyword(s):  
Random Graphs ◽  
Degree Sequence

scholarly journals Counting Triangles in Power-Law Uniform Random Graphs

10.37236/9239 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Pu Gao ◽  
Remco Van der Hofstad ◽  
Angus Southwell ◽  
Clara Stegehuis
Keyword(s):  
Random Graphs ◽  
Power Law ◽  
Degree Sequence ◽  
Clustering Coefficient ◽  
Linear Functions ◽  
Configuration Model ◽  
Local Clustering ◽  
Asymptotic Number ◽  
Multiple Edges ◽  
Local Clustering Coefficient

We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent $\tau\in(2,3)$. We also analyze the local clustering coefficient $c(k)$, the probability that two random neighbors of a vertex of degree $k$ are connected. We find that the number of triangles, as well as the local clustering coefficient, scale similarly as in the erased configuration model, where all self-loops and multiple edges of the configuration model are removed. Interestingly, uniform random graphs contain more triangles than erased configuration models with the same degree sequence. The number of triangles in uniform random graphs is closely related to that in a version of the rank-1 inhomogeneous random graph, where all vertices are equipped with weights, and the probabilities that edges are present are moderated by asymptotically linear functions of the products of these vertex weights.

scholarly journals Power-law decay of the degree-sequence probabilities of multiple random graphs with application to graph isomorphism

2017 ◽  
Vol 21 ◽  
pp. 235-250 ◽  
Author(s):  
Jefferson Elbert Simões ◽  
Daniel R. Figueiredo ◽  
Valmir C. Barbosa
Keyword(s):  
Random Graphs ◽  
Power Law ◽  
Degree Sequence ◽  
Graph Isomorphism ◽  
Power Law Decay

scholarly journals Karp–Sipser on Random Graphs with a Fixed Degree Sequence

2011 ◽  
Vol 20 (5) ◽  
pp. 721-741 ◽  
Author(s):  
TOM BOHMAN ◽  
ALAN FRIEZE
Keyword(s):  
Random Graphs ◽  
High Probability ◽  
Degree Sequence ◽  
Fixed Degree

Let Δ ≥ 3 be an integer. Given a fixed z ∈ +Δ such that zΔ > 0, we consider a graph Gz drawn uniformly at random from the collection of graphs with zin vertices of degree i for i = 1,. . .,Δ. We study the performance of the Karp–Sipser algorithm when applied to Gz. If there is an index δ > 1 such that z1 = . . . = zδ−1 = 0 and δzδ,. . .,ΔzΔ is a log-concave sequence of positive reals, then with high probability the Karp–Sipser algorithm succeeds in finding a matching with n ∥ z ∥ 1/2 − o(n1−ε) edges in Gz, where ε = ε (Δ, z) is a constant.

Convergence law for random graphs with specified degree sequence

2005 ◽  
Vol 6 (4) ◽  
pp. 727-748 ◽  
Author(s):  
James F. Lynch
Keyword(s):  
Random Graphs ◽  
Degree Sequence

scholarly journals Hamilton Cycles in Random Graphs with a Fixed Degree Sequence

2010 ◽  
Vol 24 (2) ◽  
pp. 558-569 ◽  
Author(s):  
Colin Cooper ◽  
Alan Frieze ◽  
Michael Krivelevich
Keyword(s):  
Random Graphs ◽  
Degree Sequence ◽  
Hamilton Cycles ◽  
Fixed Degree

SIR epidemics on random graphs with a fixed degree sequence

2012 ◽  
Vol 41 (2) ◽  
pp. 179-214 ◽  
Author(s):  
Tom Bohman ◽  
Michael Picollelli
Keyword(s):  
Random Graphs ◽  
Degree Sequence ◽  
Fixed Degree

scholarly journals Subgraph counts for dense random graphs with specified degrees

2020 ◽  
pp. 1-38
Author(s):  
Catherine Greenhill ◽  
Mikhail Isaev ◽  
Brendan D. McKay
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Spanning Trees ◽  
Degree Sequence ◽  
Complex Function ◽  
Random Permutation ◽  
Expected Number ◽  
Asymptotic Expressions ◽  
Number Of Spanning Trees

Abstract We prove two estimates for the expectation of the exponential of a complex function of a random permutation or subset. Using this theory, we find asymptotic expressions for the expected number of copies and induced copies of a given graph in a uniformly random graph with degree sequence(d 1 , …, d n ) as n→ ∞. We also determine the expected number of spanning trees in this model. The range of degrees covered includes d j = λn + O(n1/2+ε) for some λ bounded away from 0 and 1.

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