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Title
Maximum-entropy networks : pattern detection, network reconstruction and graph combinatorics / Tiziano Squartini, Diego Garlaschelli.
ISBN
9783319694382 (electronic book)
3319694383 (electronic book)
3319694367
9783319694368
Published
Cham, Switzerland : Springer, [2017]
Copyright
©2017
Language
English
Description
1 online resource (xii, 116 pages) : illustrations.
Item Number
10.1007/978-3-319-69438-2 doi
Call Number
QC1-QC999
Dewey Decimal Classification
621
Summary
This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem of network reconstruction and introduces various advanced techniques to reliably infer the topology of a network from partial local information. Chapter 5 is devoted to the reformulation of certain "hard" combinatorial operations, such as the enumeration and unbiased sampling of graphs with given constraints, within a "softened" maximum-entropy framework. A final chapter offers various overarching remarks and take-home messages. By requiring no prior knowledge of network theory, the book targets a broad audience ranging from PhD students approaching these topics for the first time to senior researchers interested in the application of advanced network techniques to their field.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Resource, viewed February 1, 2018.
Series
SpringerBriefs in complexity.
Available in Other Form
Print version: 9783319694368
Introduction
Maximum-entropy ensembles of graphs
Constructing constrained graph ensembles: why and how?
Comparing models obtained from different constraints
Pattern detection
Detecting assortativity and clustering
Detecting dyadic motifs
Detecting triadic motifs
Some extensions to weighted networks
Network reconstruction
Reconstructing network properties from partial information
The Enhanced Configuration Model
Further reducing the observational requirements
Graph combinatorics
A dual route to combinatorics?
'Soft' combinatorial enumeration
Quantifying ensemble (non)equivalence
Breaking of equivalence between ensembles
Implications of (non)equivalence for combinatorics
"What then shall we choose?" Hardness or softness?
Concluding remarks.
