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.
