Maximum-Entropy Networks Pattern Detection, Network Reconstruction and Graph Combinatorics /

• Main Authors: Squartini, Tiziano (Author), Garlaschelli, Diego (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: SpringerBriefs in Complexity,
• Subjects: Physics.; System theory.; Graph theory.; Complexity, Computational.; Applications of Graph Theory and Complex Networks.; Statistical Physics and Dynamical Systems.; Complex Systems.; Graph Theory.; Complexity.

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 ma...

Table of Contents:

• 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.