Generating random networks and graphs

Generating random networks and graphs / A.C.C. Coolen, A. Annibale, E.S. Roberts.

"Generating Random Networks and Graphs' describes how to correctly and efficiently generate random networks based on certain constraints. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method."

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Bibliographic Details
Main Authors: Coolen, A. C. C. (Anthony C. C.), 1960- (Author), Annibale, A. (Alessia) (Author), Roberts, E. S. (Ekaterina S.) (Author)
Format: eBook
Language:English
Published: Oxford : Oxford University Press, 2017.
Edition:First edition.
Subjects:
Random graphs.
MATHEMATICS > General.
Random graphs
Online Access:Click for online access
Table of Contents:
  • Cover; Preface; Acknowledgements; Contents; Part I The basics; 1 Introduction; 2 Definitions and concepts; 2.1 Definitions of graphs and their local characteristics; 2.2 Macroscopic characterizations of graphs; 2.3 Solutions of exercises; 3 Random graph ensembles; 3.1 The Erdös-Rényi graph ensemble; 3.2 Graph ensembles with hard or soft topological constraints; 3.3 The link between ensembles and algorithms; 3.4 Solutions of exercises; Part II Random graph ensembles; 4 Soft constraints: exponential random graph models; 4.1 Definitions and basic properties of ERGMs.
  • 4.2 ERGMs that can be solved exactly; 4.3 ERGMs with phase transitions: the two-star model; 4.4 ERGMs with phase transitions: the Strauss (triangle) model; 4.5 Stochastic block models for graphs with community structure; 4.6 Strengths and weaknesses of ERGMs as null models; 4.7 Solutions of exercises; 5 Ensembles with hard constraints; 5.1 Basic properties and tools; 5.2 Nondirected graphs with hard-constrained number of links; 5.3 Prescribed degree statistics and hard-constrained number of links; 5.4 Ensembles with prescribed numbers of links and two-stars.
  • 5.5 Ensembles with constrained degrees and short loops; 5.6 Solutions of exercises; Part III Generating graphs from graph ensembles; 6 Markov Chain Monte Carlo sampling of graphs; 6.1 The Markov Chain Monte Carlo sampling method; 6.2 MCMC sampling for exponential random graph models; 6.3 MCMC sampling for graph ensembles with hard constraints; 6.4 Properties of move families
  • hinge flips and edge swaps; 6.5 Solutions of exercises; 7 Graphs with hard constraints: further applications and extensions; 7.1 Uniform versus non-uniform sampling of candidate moves.
  • 7.2 Graphs with a prescribed degree distribution and number of links; 7.3 Ensembles with controlled degrees and degree correlations; 7.4 Generating graphs with prescribed degrees and correlations; 7.5 Edge swaps revisited; 7.6 Non-uniform sampling of allowed edge swaps; 7.7 Non-uniform sampling from a restricted set of moves: a hybrid MCMC algorithm; 7.8 Extensions to directed graphs; 7.9 Solutions of exercises; Part IV Graphs defined by algorithms; 8 Network growth algorithms; 8.1 Configuration model; 8.2 Preferential attachment and scale-free networks; 8.3 Analyzing growth algorithms.
  • 8.4 Solutions of exercises; 9 Specific constructions; 9.1 Watts-Strogatz model and the 'small world' property; 9.2 Geometric graphs; 9.3 Planar graphs; 9.4 Weighted graphs; 9.5 Solutions of exercises; Part V Further topics; 10 Graphs on structured spaces; 10.1 Temporal networks; 10.2 Multiplex graphs; 10.3 Networks with labelled nodes; 10.4 Relations and connections between models; 10.5 Solutions of exercises; 11 Applications of random graphs; 11.1 Power grids; 11.2 Social networks; 11.3 Food webs; 11.4 World Wide Web; 11.5 Protein-protein interaction networks; Key symbols and terminology.

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