Limit laws for the number of triangles in the generalized random graphs with random node weights

2020 ◽  
Vol 161 ◽  
pp. 108733
Author(s):  
Qun Liu ◽  
Zhishan Dong
Keyword(s):  
Random Graphs ◽  
Limit Laws ◽  
Random Node

THE ZAGREB INDICES OF RANDOM GRAPHS

2013 ◽  
Vol 27 (2) ◽  
pp. 247-260 ◽  
Author(s):  
Qunqiang Feng ◽  
Zhishui Hu ◽  
Chun Su
Keyword(s):  
Asymptotic Normality ◽  
Random Graphs ◽  
Joint Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Limit Laws ◽  
Zagreb Indices ◽  
Necessary And Sufficient

Several limit laws for the Zagreb indices of the classical Erdös–Rényi random graphs are investigated in this paper. We have obtained the necessary and sufficient condition for the asymptotic normality of the two Zagreb indices (suitably normalized), as well as the explicit values for the means and variances of both the indices. Besides, the limiting joint distribution of the numbers of paths of various lengths is also studied under several conditions.

Limit laws for UGROW random graphs

2013 ◽  
Vol 83 (12) ◽  
pp. 2607-2614 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Random Graphs ◽  
Limit Laws

Limit laws in the generalized random graphs with random vertex weights

2014 ◽  
Vol 89 ◽  
pp. 65-76 ◽  
Author(s):  
Zhishui Hu ◽  
Wei Bi ◽  
Qunqiang Feng
Keyword(s):  
Random Graphs ◽  
Limit Laws

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

Random Graphs

1998 ◽  
Author(s):  
V. F. Kolchin
Keyword(s):  
Random Graphs

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

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