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

ISBN-13: 9783319694368 / Angielski / Miękka / 2017 / 116 str.

Tiziano Squartini; Diego Garlaschelli

Opis

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.

Spis treści

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.