Social and economic networks.

*(English)*Zbl 1149.91051
Princeton, NJ: Princeton University Press (ISBN 978-0-691-13440-6/hbk). xiii, 504 p. (2008).

This book provides a comprehensive study of social networks. It is divided in four parts and 13 chapters, exploring the fundamentals of network analysis, models of network formation, implications of network structure and methods for empirical analysis of social networks.

The first three chapters present an outline of what social networks are, ways of representing networks and their properties, the fundamentals of graph theory and the structure of social networks. This is followed by three chapters studying random networks and their characteristics, several relevant mathematical theorems and models for network growth and strategic formation.

In the third part of the book, consisting of four chapters, several useful social network structures are examined. This includes the Bass model, models for the spread of information and disease, the theory behind learning in networks (e.g., DeGroot model) and observational learning. Several models for games on networks are then studied as well as models involving networked markets.

The last part of this book concentrates on stability and equilibrium issues as well as cooperative game theory and communication games and a discussion on measuring social interaction. Each chapter further contains a large collection of exercises for the interested reader and the book concludes with an index and a list of useful references.

The first three chapters present an outline of what social networks are, ways of representing networks and their properties, the fundamentals of graph theory and the structure of social networks. This is followed by three chapters studying random networks and their characteristics, several relevant mathematical theorems and models for network growth and strategic formation.

In the third part of the book, consisting of four chapters, several useful social network structures are examined. This includes the Bass model, models for the spread of information and disease, the theory behind learning in networks (e.g., DeGroot model) and observational learning. Several models for games on networks are then studied as well as models involving networked markets.

The last part of this book concentrates on stability and equilibrium issues as well as cooperative game theory and communication games and a discussion on measuring social interaction. Each chapter further contains a large collection of exercises for the interested reader and the book concludes with an index and a list of useful references.

Reviewer: Efstratios Rappos (Athens)

##### MSC:

91D30 | Social networks; opinion dynamics |

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91A43 | Games involving graphs |

91B74 | Economic models of real-world systems (e.g., electricity markets, etc.) |

90B10 | Deterministic network models in operations research |