scholarly journals Graph limits of random graphs from a subset of connected k ‐trees

2018 ◽  
Vol 55 (1) ◽  
pp. 125-152 ◽  
Author(s):  
Michael Drmota ◽  
Emma Yu Jin ◽  
Benedikt Stufler
Keyword(s):  
Random Graphs ◽  
Graph Limits

scholarly journals Emergent Structures in Large Networks

2013 ◽  
Vol 50 (03) ◽  
pp. 883-888 ◽  
Author(s):  
David Aristoff ◽  
Charles Radin
Keyword(s):  
Phase Transition ◽  
Large Class ◽  
Random Graph ◽  
Random Graphs ◽  
Essential Feature ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Graph Limits ◽  
Exponential Random Graph

We consider a large class of exponential random graph models and prove the existence of a region of parameter space corresponding to the emergent multipartite structure, separated by a phase transition from a region of disordered graphs. An essential feature is the formalism of graph limits as developed by Lovász et al. for dense random graphs.

scholarly journals Quasi-random graphs and graph limits

2011 ◽  
Vol 32 (7) ◽  
pp. 1054-1083 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Random Graphs ◽  
Graph Limits

scholarly journals Emergent Structures in Large Networks

2013 ◽  
Vol 50 (3) ◽  
pp. 883-888 ◽  
Author(s):  
David Aristoff ◽  
Charles Radin
Keyword(s):  
Phase Transition ◽  
Large Class ◽  
Random Graph ◽  
Random Graphs ◽  
Essential Feature ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Graph Limits ◽  
Exponential Random Graph

We consider a large class of exponential random graph models and prove the existence of a region of parameter space corresponding to the emergent multipartite structure, separated by a phase transition from a region of disordered graphs. An essential feature is the formalism of graph limits as developed by Lovász et al. for dense random graphs.

scholarly journals An example of graph limits of growing sequences of random graphs

2013 ◽  
Vol 4 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Svante Janson ◽  
Simone Severini
Keyword(s):  
Random Graphs ◽  
Graph Limits

scholarly journals More on quasi-random graphs, subgraph counts and graph limits

2015 ◽  
Vol 46 ◽  
pp. 134-160 ◽  
Author(s):  
Svante Janson ◽  
Vera T. Sós
Keyword(s):  
Random Graphs ◽  
Graph Limits

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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