scholarly journals On the Degree Sequence of an Evolving Random Graph Process and Its Critical Phenomenon

2009 ◽  
Vol 46 (4) ◽  
pp. 1213-1220 ◽  
Author(s):  
Xian-Yuan Wu ◽  
Zhao Dong ◽  
Ke Liu ◽  
Kai-Yuan Cai
Keyword(s):  
Random Graph ◽  
Degree Distribution ◽  
Critical Phenomenon ◽  
Degree Sequence ◽  
Edge Deletion ◽  
Specific Parameter

In this paper we focus on the problem of the degree sequence for a random graph process with edge deletion. We prove that, while a specific parameter varies, the limit degree distribution of the model exhibits critical phenomenon.

scholarly journals On the Degree Sequence of an Evolving Random Graph Process and Its Critical Phenomenon

2009 ◽  
Vol 46 (04) ◽  
pp. 1213-1220
Author(s):  
Xian-Yuan Wu ◽  
Zhao Dong ◽  
Ke Liu ◽  
Kai-Yuan Cai
Keyword(s):  
Random Graph ◽  
Degree Distribution ◽  
Critical Phenomenon ◽  
Degree Sequence ◽  
Edge Deletion ◽  
Specific Parameter

In this paper we focus on the problem of the degree sequence for a random graph process with edge deletion. We prove that, while a specific parameter varies, the limit degree distribution of the model exhibits critical phenomenon.

Tracking a Markov-Modulated Stationary Degree Distribution of a Dynamic Random Graph

2014 ◽  
Vol 60 (10) ◽  
pp. 6609-6625 ◽  
Author(s):  
Maziyar Hamdi ◽  
Vikram Krishnamurthy ◽  
George Yin
Keyword(s):  
Random Graph ◽  
Degree Distribution ◽  
Markov Modulated

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.

scholarly journals The number of graphs and a random graph with a given degree sequence

2012 ◽  
Vol 42 (3) ◽  
pp. 301-348 ◽  
Author(s):  
Alexander Barvinok ◽  
J.A. Hartigan
Keyword(s):  
Random Graph ◽  
Degree Sequence

scholarly journals Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
István Fazekas ◽  
Bettina Porvázsnyik
Keyword(s):  
Asymptotic Behaviour ◽  
Random Graph ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Graph Model ◽  
Random Graph Model ◽  
Scale Free ◽  
Attachment Model ◽  
Law Degree

A random graph evolution mechanism is defined. The evolution studied is a combination of the preferential attachment model and the interaction of four vertices. The asymptotic behaviour of the graph is described. It is proved that the graph exhibits a power law degree distribution; in other words, it is scale-free. It turns out that any exponent in(2,∞)can be achieved. The proofs are based on martingale methods.

Acquaintance Vaccination in an Epidemic on a Random Graph with Specified Degree Distribution

2013 ◽  
Vol 50 (04) ◽  
pp. 1147-1168 ◽  
Author(s):  
Frank Ball ◽  
David Sirl
Keyword(s):  
Random Graph ◽  
Degree Distribution ◽  
Numerical Study ◽  
Branching Processes ◽  
Large Population ◽  
Configuration Model ◽  
Vaccine Response ◽  
Final Size ◽  
Infinite Type ◽  
Type Spaces

We consider a stochastic SIR (susceptible → infective → removed) epidemic on a random graph with specified degree distribution, constructed using the configuration model, and investigate the ‘acquaintance vaccination’ method for targeting individuals of high degree for vaccination. Branching process approximations are developed which yield a post-vaccination threshold parameter, and the asymptotic (large population) probability and final size of a major outbreak. We find that introducing an imperfect vaccine response into the present model for acquaintance vaccination leads to sibling dependence in the approximating branching processes, which may then require infinite type spaces for their analysis and are generally not amenable to numerical calculation. Thus, we propose and analyse an alternative model for acquaintance vaccination, which avoids these difficulties. The theory is illustrated by a brief numerical study, which suggests that the two models for acquaintance vaccination yield quantitatively very similar disease properties.

scholarly journals Phase transition on the degree sequence of a random graph process with vertex copying and deletion

2011 ◽  
Vol 121 (4) ◽  
pp. 885-895 ◽  
Author(s):  
Kai-Yuan Cai ◽  
Zhao Dong ◽  
Ke Liu ◽  
Xian-Yuan Wu
Keyword(s):  
Phase Transition ◽  
Random Graph ◽  
Degree Sequence

scholarly journals The scaling window for a random graph with a given degree sequence

2012 ◽  
Vol 41 (1) ◽  
pp. 99-123 ◽  
Author(s):  
Hamed Hatami ◽  
Michael Molloy
Keyword(s):  
Random Graph ◽  
Degree Sequence ◽  
Scaling Window
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